ELO is relative. There's no reason why a GM ELO should be 2800 or 280 or 28000. So it's all decided by ELO of every other person. So if the ELO gain/loss calculation and audience of Lichess and chess.com are exactly the same, because of different starting position, I don't think they'd converge to the same ELO but instead will differ by starting position difference.

Also I can't really prove it mathematically but I guess average ELO would also hover on the starting ELO. Because I can't see why it would hover anywhere else and any ELO gained would be lost by someone else.