I would use a dynamic reader (ie one with just a single source feature type with the merge filter set). Then expose the fme_feature_type format attribute. This will give you the name of the table being read.
You can run the data through a DuplicateRemover too, removing duplicate values for fme_feature_type, in order to get a list of unique table names.
There is a Schema format that returns the schema of a dataset, but I think it works only with file-based data, and wouldn't work with a File Geodatabase (though it might with a Personal Geodatabase).
I do think that in a case like this there's very little reason to not have the parent workspace run the worker on FME Server itself using an FMEServerJobSubmitter transformer. Having the parent use a SystemCaller to run a bat file to run the worker workspace on Desktop just seems an odd way of doing things.
Best Answer
I'm just getting started with FME, and am using a shutdown script to copy my target FGDB to another location and to save out the log file:
That's pretty basic, but there really is no limit I don't think. There are tons of ideas here as well.
EDIT: Added in code to get numbers of features written and push those out to CSV log file.