IMO it would make the conjecture far more interesting, as it would be a surprise to most people who have thought about the problem.
Many natural questions would arise, starting with “Is this the only counterexample?”
Many natural questions would arise, starting with “Is this the only counterexample?”
(I got that from https://math.stackexchange.com/questions/514/conjectures-tha... which features some other false conjectures that may be of interest to you)