As a fervent rat lover, and former owner of domesticated rats, I can firmly say that as long as you're not feeding them (and they're not being fed by people on a regular basis), they will likely be avoiding you as much as you want to avoid them. Rats keep themselves pretty clean, and while they can leave mess behind, as any animal would, I'm pretty sure Disney keeps their kitchens, and really all areas of the park, very clean, so there's nothing to worry about.
Now would I try to catch or pick up a wild rat? Heck, no. Not anywhere. It's a wild animal. But it doesn't worry me any more than a feral cat would, or a squirrel. The only reason I wouldn't be tossing it popcorn is for its own safety.
Rats get a really bad rap. They are wonderful, intelligent, loving animals.
Things That Make Me Happy 2 by
opaleyes, on Flickr