While the exact times aren't available, OP was done the favor of being boarded after the flight was fully boarded (OP's words).

No, the FA should not be running around looking to see if there's OH space and delaying the push.

While it would be better during the normal boarding process for the FA's to call or otherwise signal upfront when the OH's really are full, on this last second stuff, I'd rather push ontime than hold and lose the departure slot. Nobody knows if Operations was advising the Captain and thus the cabin crew that they needed to hotfoot it out.