Yes they'll do that, Claire, but you will have to wait for the bellhop to collect it from your room before checking out, and for it to be delivered to the next room once you're in (I guess that's more about the bellhops getting their tips than anything else).
Once we've checked out of one resort, we always go straight to the next to check in on the basis that we should get a better choice of room by doing it early. Invariably, the room isn't ready, but you'll get your Keys to the Magic cards and you can call back later to check progress on your room.