I wouldn’t think anything would happen because the egg has a shell. I would imagine that the shell is unlike a cell membrane because its job is to not allow substances in. Accordingly, it would not have any properties of a cell membrane; low permeability and protein channels absent would mean that processes such as osmosis, diffusion, active transport wouldn’t be possible. Effectively, water can’t move in or out so the egg won’t shrink and shrivel up or swell and burst due to the movement of water out or into the egg (cell) respectively.