Hi all.
I worked at Disney World doing an internship from January-May of '06. I worked at Splash Mountain controlling the ride and all that jazz. I really wouldn't recommend bringing a Coach bag to the World. I can't tell you how many times ladies complained that their bag got wet on Splash or how many other times I saw stuff get spilled on bags, other people walking past and hitting/spilling stuff on bags...
There is one bag that's sort of like the be-all and end-all bag that's discussed on a Disney forum - The Bagallini. True, it's not Coach, but it is the BEST when it comes to organizing and keeping your hands free. The messenger bag is light but it's also big enough for everything you need and everything you never knew you needed.
Just a suggestion.

I've never carried any of my Coach bags while in the parks. Too much can happen to them. Thank goodness nothing's happened to any of the abover posters' bags! Also, I agree with GOTRACEY - Disney just isn't the place to show your flashy, gorgeous Coach pieces. Keep those babies safe and out of harm's way!
EDIT: Regarding Crowds -
Sort of O.T. - The first 2 weeks in December are the BEST time to go to the World. No crowds, everything's decorated for Christmas and the holiday shows are going on. If you're going the week of/after Christmas and New Year's... Good luck. It's a mad house. Wall-to-wall people.