What do you reckon? Personally, I think this seems more plausible than it would be to assume that Enterprise and her crew were actively undertaking regular missions during that short period of time, and at that particular stage in their careers.
TUC does indeed indicate that the crew is being reassembled after some time; Sulu has been in command of the Excelsior
for 3 years, and McCoy hasn't missed him ("If we're all here, where's Sulu?"). It therefore seems unlikely that the full Enterprise
-A crew has been on active duty together on that ship within the previous three years.