I'm not a boater, but what folks with experiene in Belize waters tell me is that you can do it, but that you'll have to be careful. There are a considerable number of places in northern Belize where a 5 foot+ draft is going to be a problem, and you do not want to spend a lot of time dragginga limestone bottom.
Farther south, the water is generally deeper.
You can probably get some expert advice on this board or on the belize.net forums (Hugh Parkey there is a divemaster who knows Belize waters well.) You certainly need local advice and the best charts you can find.
Belize First Magazine http://www.belizefirst.com/