FMGo does not allow plugins, so FMGo is limited to what can be added.
I would use dropbox over iTunes to move files between devices. In your situation, I would suggest using a solution such a "One-Click" One-Click Version Updates for FileMaker Go 13 | Colibri Solutions
If the downstream workflow could involve FileMaker Pro 14, instead of zip archiving the many files, perhaps you could deliver a simple FileMaker Pro file with the files embedded inside container fields (one table with a file per record). FileMaker Go can export to a FileMaker file, and you should be able to automate filling in the container fields via scripting.
Then the user would only have one file, a FileMaker file, to pull out of iTunes. The recipient in the workflow could open up the FileMaker file and run a script to Export Field Contents to get all of the files.