Certainly one can
cruise the Bahamas in most any boat. However, I've cruised in personal and
charter boats ranging from 2 feet to just over 5. Five+ is much more restrictive. Many harbours and cuts have a 3.5 MLW entrance. With a 3 foot boat you can come and go anytime you please. With 5, you are limited to high tide.
Similarly, many of the bays I've anchored in are around 5 feet MLW. Shallower draft is the difference between being tucked away and being out in the slop all night.
Also to consider, is what interests you. If your main interest is towns and resorts, draft is less of an issue than when exploring the uninhabited islands.
I have a
monohull, but if I had about 100K to spend for a Bahamas boat, I'd be looking at catamarans.
My first Bahamas boat was a
bilge keel monohull and that offered a reasonably low draft for a Bahamas boat as well.
In short, when it comes to attributes for a Bahamas boat, I put draft as a prime consideration.