I lived in Bahamas for a year.
Some places you can get into. Some you cannot.
For example, Man O' War harbour in Abacos.. you will not make it. But you can anchor
outside the harbour and most of the time will be okay.
Almost always, if you cannot get in somewhere, you can find a place nearby that you can anchor
at, maybe you will have to dinghy
in, maybe not be as protected.. Or you might have to take a deviation. I advise you to get charts
such as the Explorer charts
and see for yourself.
If you will notice, I am spelling "harbour" in the British style. Just as you are calling it "draught" instead of "draft." See how polite I am.