I would think that trying to chain it to a lampost in a parking lot could easily get the bike hit by a bus or other car, some of the busses have to make some tight turns as it is. But, to be sure, you should probably just call or email Disney and ask. Maybe they do have some place to store it that is slightly backstage, like an employee parking area, or something. But remember, the entrance road to EPCOT, and some the other parks, has a LOT of traffic, and is designed more like a mini-freeway system, with on ramps/off ramps rather than like a regular city road surface street system.
I think it would be quite dangerous to ride a bicycle anywhere except inside a resort like the Campgrounds, OKW or SSR.
I think I have seen a bike rack at Downtown Disney, though.