How would they keep them out? It's not like you can spray for them, as they do with mosquitoes. And Disney doesn't really keep the other pests out. At WDW, you'll find poisonous snakes, poisonous spiders, lizards, rats, mice, you name it, and that's just at the resorts. Anything potentially dangerous is removed when it's found, but they certainly can't get them all.
There's 40+ square miles of land there, most of it undeveloped woods or swamp. Even if they somehow managed to remove every single alligator on the property, within a week there would be more, unless they put a fence around all of WDW. Which would be like putting a fence around Boston.