I would think no. I would expect (but have no actual knowledge) that they generally grant a certain percentage of the prizes each day - sort of space things out evenly. So it's not likely, but not impossible, that there'd be a big glut of last-minute prizes awarded. Even if that were to happen, it would be the "regular" stuff - the ears, the lanyards, that kind of thing. Since the Dream FastPasses are dated, they would tend to have X amount with each day's date, and none dated after 12/31/08.