it is possible, but I'd rate it as highly inefficient. You have been warned.

working for objects and SQL

/// The company this employee works for.
Relationship Company As Company [ Cardinality = one, Inverse = Employees ];

Property Cname As %String [ Calculated, SqlComputeCode =
    {set {*}=##class(Company).%OpenId({Company}).Name }, SqlComputed ];

running the docker image uncovered the result (interactive:=> docker-compose up)   
only at stopping of the container.  So I changed installer.sh and run the method from iris session

This gave me the full dimension of this EXCELLENT TOOL!  especially the integrity check!
I just can say WOW. 
So delegating of routine jobs of a System Manager becomes safe and easy.

This is the output that kicked me:

-------------------------------------------------------------------------------
irisowner@7aa9b053e544:/opt/irisapp$ iris session iris -U "%SYS" 
Node: 7aa9b053e544, Instance: IRIS
%SYS>do ##class(BackupChecker.Installer).restoreAll("backup.cbk")
Starting to restore the Backup... It will take some time, be patient!
The following directories will be restored:
c:\intersystems\iris\mgr\appcode\ =>
                         /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/
c:\intersystems\iris\mgr\appdata\ =>
                         /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/
c:\intersystems\iris\mgr\cacheuser\ =>
                       /ISC/utiles/Restore/c:\intersystems\iris\mgr\cacheuser\/
c:\intersystems\iris\mgr\remote\ =>
                          /ISC/utiles/Restore/c:\intersystems\iris\mgr\remote\/
c:\intersystems\iris\mgr\user\ =>
                            /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/ Cannot mount database in /ISC/utiles/Restore/c:\intersystems\iris\mgr\cacheuser\/ because
its default collation is not available (see messages.log).
c:\intersystems\iris\mgr\cacheuser\ will not be restored. Cannot mount database in /ISC/utiles/Restore/c:\intersystems\iris\mgr\remote\/ because
its default collation is not available (see messages.log).
c:\intersystems\iris\mgr\remote\ will not be restored. ***Restoring c:\intersystems\iris\mgr\appcode\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/ at 10:18:55
469 blocks restored in 0.0 seconds for this pass, 469 total restored. ***Restoring c:\intersystems\iris\mgr\appdata\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/ at 10:18:55
413 blocks restored in 0.0 seconds for this pass, 413 total restored. Starting skip of c:\intersystems\iris\mgr\cacheuser\.      skipped 77 blocks in .007096 seconds. Starting skip of c:\intersystems\iris\mgr\remote\.      skipped 77 blocks in .006635 seconds. ***Restoring c:\intersystems\iris\mgr\user\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/ at 10:18:55
656 blocks restored in 0.1 seconds for this pass, 656 total restored. ***Restoring c:\intersystems\iris\mgr\appcode\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/ at 10:18:55
1 blocks restored in 0.0 seconds for this pass, 470 total restored. ***Restoring c:\intersystems\iris\mgr\appdata\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/ at 10:18:55
1 blocks restored in 0.0 seconds for this pass, 414 total restored. Starting skip of c:\intersystems\iris\mgr\cacheuser\.      skipped 1 blocks in .000007 seconds. Starting skip of c:\intersystems\iris\mgr\remote\.      skipped 1 blocks in .000008 seconds. ***Restoring c:\intersystems\iris\mgr\user\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/ at 10:18:55
1 blocks restored in 0.0 seconds for this pass, 657 total restored. ***Restoring c:\intersystems\iris\mgr\appcode\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/ at 10:18:55
1 blocks restored in 0.0 seconds for this pass, 471 total restored. ***Restoring c:\intersystems\iris\mgr\appdata\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/ at 10:18:55
1 blocks restored in 0.0 seconds for this pass, 415 total restored. Starting skip of c:\intersystems\iris\mgr\cacheuser\.      skipped 1 blocks in .000022 seconds. Starting skip of c:\intersystems\iris\mgr\remote\.      skipped 1 blocks in .000008 seconds. ***Restoring c:\intersystems\iris\mgr\user\ to /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/ at 10:18:55
1 blocks restored in 0.0 seconds for this pass, 658 total restored. Mounting /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/
    /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/  ... (Mounted) Mounting /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/
    /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/  ... (Mounted) Mounting /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/
    /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/  ... (Mounted) 
[Journal not applied to any directory] 
Restored completed!

Starting the Integrity report
Directory: /ISC/install/mgr/
No errors found
Summary of blocks in /ISC/install/mgr/         87 Pointer Level blocks         696kb (16% full)
     5,908 Data Level blocks             46MB (84% full)
     2,553 Big String blocks             19MB (86% full) # = 1,011
     8,563 Total blocks                  66MB (84% full)
     2,951 Free blocks                   23MB Elapsed time = 14.3 seconds. Directory: /ISC/install/mgr/irisaudit/
No errors found
Summary of blocks in /ISC/install/mgr/irisaudit/         34 Pointer Level blocks         272kb (0% full)
        54 Data Level blocks            432kb (33% full)
         4 Big String blocks             32kb (99% full) # = 1
       107 Total blocks                 856kb (20% full)
        21 Free blocks                  168kb Elapsed time = 6.1 seconds. Directory: /ISC/install/mgr/irislocaldata/
No errors found
Summary of blocks in /ISC/install/mgr/irislocaldata/         35 Pointer Level blocks         280kb (1% full)
       213 Data Level blocks           1704kb (58% full)
        25 Big String blocks            200kb (74% full) # = 13
       288 Total blocks                2304kb (49% full)
     1,130 Free blocks                 9040kb Elapsed time = 6.5 seconds. Directory: /ISC/install/mgr/iristemp/
No errors found
Summary of blocks in /ISC/install/mgr/iristemp/         46 Pointer Level blocks         368kb (0% full)
        81 Data Level blocks            648kb (33% full)
         0 Big String blocks
       142 Total blocks                1136kb (19% full)
     1,177 Free blocks                 9416kb Elapsed time = 8.5 seconds. Directory: /ISC/install/mgr/user/
No errors found
Summary of blocks in /ISC/install/mgr/user/         50 Pointer Level blocks         400kb (0% full)
        73 Data Level blocks            584kb (27% full)
         0 Big String blocks
       138 Total blocks                1104kb (14% full)
     1,270 Free blocks                10160kb Elapsed time = 8.9 seconds. Directory: /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/
No errors found
Summary of blocks in /ISC/utiles/Restore/c:\intersystems\iris\mgr\appcode\/         32 Pointer Level blocks         256kb (2% full)
       379 Data Level blocks           3032kb (71% full)
        43 Big String blocks            344kb (88% full) # = 12
       469 Total blocks                3752kb (66% full)
     1,067 Free blocks                 8536kb Elapsed time = 0.1 seconds. Directory: /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/
No errors found
Summary of blocks in /ISC/utiles/Restore/c:\intersystems\iris\mgr\appdata\/         57 Pointer Level blocks         456kb (0% full)
       241 Data Level blocks           1928kb (66% full)
       100 Big String blocks            800kb (92% full) # = 30
       413 Total blocks                3304kb (61% full)
       995 Free blocks                 7960kb Elapsed time = 0.1 seconds. Directory: /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/
No errors found
Summary of blocks in /ISC/utiles/Restore/c:\intersystems\iris\mgr\user\/         68 Pointer Level blocks         544kb (1% full)
       447 Data Level blocks           3576kb (70% full)
       126 Big String blocks           1008kb (90% full) # = 33
       656 Total blocks                5248kb (65% full)
       752 Free blocks                 6016kb Elapsed time = 0.2 seconds. Directory: /usr/irissys/mgr/enslib/
No errors found
Summary of blocks in /usr/irissys/mgr/enslib/        130 Pointer Level blocks        1040kb (33% full)
    14,684 Data Level blocks            114MB (97% full)
     4,407 Big String blocks             34MB (88% full) # = 1,606
    19,236 Total blocks                 150MB (94% full)
     1,500 Free blocks                   11MB Elapsed time = 12.6 seconds. Directory: /usr/irissys/mgr/irislib/
No errors found
Summary of blocks in /usr/irissys/mgr/irislib/        180 Pointer Level blocks        1440kb (60% full)
    39,001 Data Level blocks            304MB (98% full)
    11,177 Big String blocks             87MB (86% full) # = 4,234
    50,373 Total blocks                 393MB (95% full)
        59 Free blocks                  472kb Elapsed time = 7.9 seconds. Directory: /usr/irissys/mgr/zpm/
No errors found
Summary of blocks in /usr/irissys/mgr/zpm/         44 Pointer Level blocks         352kb (11% full)
     2,129 Data Level blocks             16MB (97% full)
       453 Big String blocks           3624kb (88% full) # = 175
     2,641 Total blocks                  20MB (94% full)
       431 Free blocks                 3448kb Elapsed time = 7.7 seconds. Run successfully and found NO errors! 
Databases are VALIDATED!
%SYS>
-------------------------------------------------------------------------------
callSQL ;
 ; compose an SQL Statement
 set query="SELECT something FROM TABLE_A JOIN TABLE_B ON ...........WHERE ...."  
 set rs=##class/%ResultSet.%NEW()
 set sc=rs.Prepare(query)
 if 'sc write $system.OBJ.DisplayError(sc)
 set sc=rs.Execute()
 if 'sc write $system.OBJ.DisplayError(sc)
 while rs.%Next() {
    ;consume the result set  row by row
}

OK yo can write this in .INT, in .MAC, in Methods .....

and SORRY:
IDX is still just 3 chars to me, as Athena is 6 chars. (or the Greek Godess of Wisdom)

BIG CONGRATULATIONS to the team that made this possible!

When I joined ISC ~20 years ago I was shocked that there was no exchange
of information and code between customers. There was just nothing.
As SSE I met customers that didn't know of each other just living within a mile's distance.

I made noise and rumors and proposals to change this.
Located in Vienna(Austria, EU) with no local office I had zero influence.
I was like an alien from the outer edge of the milky way.

Only 4 years ago, 3  years after my retirement from ISC, and just by accident, I met the Community.  
I'm happy that "my personal" dream became so successful true.
Thanks to the amazing team and their many ideas that move the Community forward. 

There is a basic mistake:
docs refer to "Indexing a JSON Object aka  %DynamicObject 
But in your example, you use %Stream.GlobalCharacter  which is a totally different object
The fact that it contains a JSON formatted string is not visible from the outside of the stream.
Instead of writing it to the Stream (which is an overkill anyhow) convert it and store it as JSON Object. 
That's what I had to do in my example

OK. I was blocked by other activities. But this is my solution:
Assumption1:    Property JSON As %Stream.GlobalCharacter;
Assumption2:    You know the properties you want to index, as with normal tables 
The idea: A calculated property is mainly used for building indices 
The solution: the Stream needs to be presented as %DynamicObject to get the value.
 And here is it:

Property JSON As %Stream.GlobalCharacter;

Property FirstName As %String [ Calculated, SqlComputed ,
         SqlComputeCode = { set {*}=..GetDyn({ID},"FirstName") } ];

Property LastName As %String [ Calculated, SqlComputed ,
         SqlComputeCode = { set {*}=..GetDyn({ID},"LastName") } ];

Index fn on FirstName;
Index ln on LastName;

ClassMethod GetDyn(ID As %Integer, item = "") As %String
{
   set JSON=..%OpenId(ID).JSON
   do JSON.Rewind()
   set st=JSON.Read(3000000)
   set dyno={}.%FromJSON(st)
   set rep=$Property(dyno,item)
   quit rep
}

There is room to improve the speed of the method.    
Also saving your keys in individual properties during data load could be a valid approach.
The principle is always the same. %Stream --> %DynamicObject --> extract keys by name