Can a tournament allowed to run if all players are allowed to cheat? I am interested to know whether money based online chess tournament would succeed if all players are allowed to cheat.
This concept is called advanced chess or freestyle chess.

There used to be an advances chess tournament in Leon already in the late nineties. Nowadays it has reverted to a normal rapid tournament.

And there have been freestyle tournaments online (for money), first organised by chessbase and nowadays apparently continued by Infinity Chess.