I just got back from the Majesty, and yes, you have to clear customs or immigration (can't remember what it was called exactly) before you get off the ship in Key West. The night before, your deck is assigned a time for the next morning to do this. The time is not strict - you can go whenever you want.
The ship, the food, service and everything was nice. I even enjoyed it with all the spring break college kids (there were about 1500 of them) - I didn't let it bother me. I can imagine that the environment would be completely different at a different time of the year.