I doubt the cat would mind. I knew a cat who had been raised in a cage and when he became a pet he found the toaster and the stove burner were acceptable litter boxes. (ugh, yuccch) However, you might want to be sure the "up" box is on a non-slip surface, like that rubbery mesh they put under throw rugs. Or you could use Quake Putty or Museum Wax if you don't have to move the box often.
What a mess if the box fell to the floor - probably that cat would never use that box again no matter what. Can't blame him.