As others have indicated, most of the time when Disney overbooks, they contact people by email well in advance of their trip and offer them the upgrade.
I've also seen anecdotes of people who have booked a particular room category, had it not available at check-in and not being offered an "upgrade" at all.
Anything can happen.
Now depending on your category, you could try playing dumb and requesting a particular building at check-in, even though you know there aren't any rooms in your category.
ie. I'm booked standard view at POFQ and I could request Bldg 5 or 6, even though I know that all the rooms in those buildings are water or garden view.
Granted, I specifically booked standard, because I DON'T want to be in either one of those buildings. I'm actually a little worried that I'm going to get the single standard view room in building 2.
Anyways...in your case, you could request Oak Manor, even though all those rooms are Royal Rooms etc.
Being upgraded to a different resort is very rare, and I doubt they would be looking for people at check-in.