Carol wore a Starfleet uniform in STID, and was (IIRC) addressed as Lieutenant, so that tends to be a giveaway.
Since STID never told us that Carol was lying about being in Starfleet, I think it's safe to assume that she was genuinely in Starfleet.But since that was a sham, it might be that Carol's keel-hauling for stealing the uniform was postponed until the conclusion of the adventure, and in actual fact she was but a cunning civilian with access to daddy's uniform fabricator...
As to whether or not Prime Universe Carol was ever in Starfleet, I can honestly see it either way. She's certainly sympathetic to them ("Starfleet has kept the peace for a hundred years. I cannot and will not subscribe to your interpretation of this event!"), so I could see her being a member in her younger days before she decided it wasn't for her. This also provides a convenient explanation for how she & Kirk could have met.