No, unless one was built in the last few weeks, no hotel pools on the island. There was talk of Iguana Reef Inn adding a pool, but it hasn't happened yet.
From our trip to Caye Caulker, the accomodations are VERY basic. There might be one or two "fancier" ones but if you're looking for a resort-type place with a pool you would probably have better luck on Ambergris Caye.