yes, group id should work... You can see this test:
This is the bpmn file it uses:
By emulating your example, I was able to get my example to work. So that answers my inquiry.
However, the small changes I made so that my example is closer to yours don't seem to explain why mine didn't work before:
1.) I had been using a script task to initialize the value for the "group" process variable, whereas you are passing it as a parameter when creating the process instance. So I removed the script task and took the parameter approach (which I would have probably done at the outset if I'd had more experience).
2.) In the Process Editor dialog for specifying the "group" process variable, I specified the the Type as object with class name String (as you had done). However, now that I look at this again, I can see it has somehow reverted back to "Object".