The running joke in Florida is that if you leave water in your Bathtub for to long a gator will find it...
Anywhere you have fresh water you will find gators. Keep in mind a gators natural instinct is to be fearful of people. That is why it is illegal to feed an alligator. When people feed them, they lose their fear and will become to accustomed to humans and come to them for food.
With that said, yes, there are many alligators on Disney property. Disney will leave them alone until they get to a certain size (or too aggressive) and then they will trap them and relocate them. We have alligators on the Rivers of America in MK all the time (although the trappers do come get those before they are fully grown), but they generally stay on the backside of the river between Big Thunder and Haunted Mansion where there are no people. When the Riverboat is running you can usually find them on the banks in the back while you are riding, but you will very rarely see them from the park side.