I'm not sure, but I doubt it. I can't really see Disney helping you go stay with someone else. If you don't have a car, a cab ride to the Swan would be super-cheap from the Beach Club, and you won't have to wait for the cab.
Have you switched hotels before? We did it once, and it was a major hassle (luggage aside). You have to pack up everything to move, which is a bigger chore when you're there than it is at home. And then, of course, you have to pack up again when you're going home.
If you like to take a mid-day break, you may be out of luck, because you might not be able to get into your room until 3:00.
My humble advice: pick a hotel and stick with it.
Have a great trip!