Yes, and no. I know with gamadv-xtd3 the users can create a log of their gam commands.
But they would be in the actual admin's home dir, so to get any overview you'd have to have them copy/share/upload them to some place you have access to.
gam isn't a centrally managed tool, and it can also impersonate other users, so you can't see it in the audit logs who actually did what.