I've never heard of anyone seeing one on International Drive, there simply isn't the habitat for them to live in, but, without wanting to make anyone nervous, to say 'no chance' is plain wrong
I've seen 'gators several times on Disney property....including this last trip in May where I couldn't have been more than 20 feet away from one at the Beach Club Bus Stop (there was a fence between us so there wasn't any danger being so close) - he is something of a permanent resident there and if you run a search on either the Resorts or DVC boards you'll see plenty of mentions of him! You may also find a picture of the 'gator that was spotted recently at the Magic Kingdom dock
I've also seen one at the Coronado Springs resort, sitting beside a small lake and under some room balcony's (I joke that he was waiting for lunch to fall out

) and even one by the side of the road...can't remember where that was though...I was on a Disney bus on some back road somewhere.
On the other hand, they are reclusive creatures, usually small and will usually dive straight into the water (that's always very nearby) if approached (as witnessed with the Coronado Springs 'gator when the Disney bods turned up to try and move him!) - not at all like Crocodiles who view everything that breathes as their next meal
Spiders - never seen any!
Snakes - just caught the tail of one shooting into a bush (again at the Beach Club) once but I know there have been several reports of seeing them at the Water parks.
Now...what you have to understand next is...I'm a critter lover...seeing any and all of these animals does nothing but make me happy as punch...infact I actively <i>look</i> for them! And still, my encounters with anything reptilian, in many trips, can be counted one hand *sigh*
So I'd not worry at all, whilst they certainly exist your chances of seeing something is slim, and the chances of actually getting to close to one virtually non-existant.