I guess it depends on where south is and what time of year. In the trades, AC is not necessary when at anchor. At the dock - yes. Personally, I would want to be out of there by July if living aboard. Summer, north of the Chesepeake Bay.
The Bahamas in winter, it should not be necessary. Now if your talking Florida, Bahamas in summer that is a whole different story. If you go to the Northeast US coast, you can probably get by without it at the dock on all but the hottest of days. At anchor, you should be ok for even more days.
I have AC/Heat and the only way I can run it is plugged in at the dock or running my generator.
In my case. Absolutely. I have kids and a wife who likes to be warm in winter and cool (at dock) in the summer. If I''m going to drag them down to the boat every few weeks and have them enjoy themselves, temperature control is part of the gig. On the hook, it''s cooler and we can always go for a swim. But at the marina-of-the-moment air tends to be still, and the A/C is great. Even in Florida, last week''s trip was saved from us freezing because of the A/C (as a heat pump, keeps us warm too) kept the boat toasty.
Of course, you can live without it. But it makes the trip easier for my crew, ergo more trips to the boat.
Only negative: I''ve lost the use of two hanging lockers and one settee storage area for a compressor and two evaporators. It''s worth it though.