Please excuse me if I'm wrong, but I understand that WilhelmII had a son and that son supported or at least sympathized with The Nazis.
Had the monarchy continued after WWI I doubt WilhelmII would have remained as Kaiser, that would probably have gone to his son. See above what I said about WilhelmII's son.
It would be interesting to see how Hitler would have done coming to power in a monarchist Germany. I think it depends on whether the other conditions that brought Hitler to power would still be as strong in TTL, conditions such as the economy, fear of Communism, etc.