Well, not in the downtown area.

Many of the suburban areas have bayous, canals, lakes, etc., and gators do show up in them. Some pretty big ones too.
A thing that happens fairly often is some guy catches a smallish gator and brings it home. They soon realize gators don't make the best pet, so they release it in the lagoon at the nearest park, subdivision, or golf course.
It's funny to be working a topwater bait for fish and have a three-foot gator trying to catch up to it.