Alligators maybe not, but in the one time that I have paddleboarded in the keys I saw a crocodile. Probably a crocodile rather than a gator, I didn’t get that close… but from reading articles they’ll occasionally eat a small dog around there, so they are definitely out there.

Saltwater crocs do exist in southern Florida, no doubt. And there's some chance a gator could swim from one island to another (or the mainland).

The easiest way to discern each is based on their snout. If the reptile you saw has a blunt nose about the same width as its jaw, then it's a gator. If, instead, the jaw looked more like a trapezoid, then it's a croc.

Both are opportunistic hunters capable of taking down mammals up to adult bovines or horses. The latter two examples are rare as the size of the croc/gator has to be rather large.