NOt sure on if it will. MOst pcs have the hdd lying flat even if it is a flatbed pc but dont the have then on their sides in raid arrays? The way the bearings are on it would make me think it would do some dmg over a long perions as it int supported both sides of the disc. Not sure bout it so dont take me word on it.
I would have thought that you would be better off keeping it the way it was intended to run and securing it in some way so that it will come to no harm. Shouldnt take much thought to devise a way of doing it.
Lying it down won't hurt, it just might not be very easy for a pre school kid to load cd's into it if it's tipped up. It shouldn't affect the readablity of the drives because remember the PS2 can be used vertical and works fine. Just try not to put a heavy monitor on the "top" because this is still really the side of the computer and could dent or buckle it as it's not as strong as the lid of a desktop machine.