We leave our dinghy in the water all the time in the Bahamas and have never had a problem. We also leave our boat unlocked. Unless you are in Nassau or maybe Freeport, crime rates there are considerably lower than they are in the US.
I'm not telling you to do what we do, just passing along the info, so take it for what it is worth. We've spent a total of more than a year there, mainly in the Abacos, Grand Bahama, Andros, and the Berry Islands over the last 12 years. I do put a cable and lock on the dinghy when we go to the Marsh Harbor dinghy dock, but that's the only place.
Boat theft IS an issue there, but it is mainly larger, faster, center consoles with Yamaha motors 250 hp and up. Bigsfish's above post is the first dinghy theft I've heard of there, though I'm sure it does happen occasionally.