Do little alligators bite?

I go to school in Gainesville, FL, and our mascot is the alligator. Now in central Florida you often see little baby alligators hanging out with their moms in the drainage ditches. These mom gators seem to move very slowly, so I think I could probably grab one of the babies to keep in my dorm room and run before she caught me. But will the little alligators bite? Or could I walk one around campus on a leash?