The first year I went to the Bahamas with my dog(2006), I applied (late) for the permit with the extra fee to expedite. I waited in Miami(Dinner Key) for several days, a good weather window came with no permit having arrived, so I went. I was never asked about a dog at Customs/Immigration in Bimini.
The second year I went(2007), I had my permit and went to a vet in Coconut Grove to get the Vet Certificate(I had to get a microchip for Val as there was a place on the form to put a microchip number, and the vet wouldn't sign the form without one). When I arrived at Customs/Immigration in Bimini, I was asked if I had a pet on board, and the lady working expressed appreciation that I had met the Bahamian requirements.
So basically, it's a crapshoot whether you get questioned or not. But it's not that difficult to meet their requirements, so I'd suggest doing so.
Flying Scot #768