Deffinately YES!!!
With that draft, plan on anchoring off the coast of Ft. Lauderdale, Fl. and dinghy your way to the Bahamas. When you get further east in the Carribean, it will be less of a problem, but a problem none the less. As Capt'n Dave said " just anchor out in deeper water." However, deeper water may not be far enough inside a bay or cove to get good protection. Given some of the advantages of a deep draft, i certainly wouldnt let it deter me from the trip. It just means that anchoring places will require some additional planning.Good luck, and go for it.