Actually, no, a square cover would have to have a much wider flange in order to ensure that it could not fall in . (rotated 45 degrees in relation to the whole and tipped up, a square cover would fall in)
Actually, yes, that's exactly what I was getting at. You'd have to make the square cover sqrt(2) times wider than the hole, but you could still prevent it from ever falling in. (Granted, it's not a very efficient solution, though.)