I was looking that up on Steam. You can add Max Payne as third party app in Steam, but that adds only a link. It does not allow you to download or use the steam-version. The Steam Version seams to work fine since there is no CD-Check.
I have the Original Version on CD here, and installed it. no Problem there. But i can´t start it though because of the cd check. I tried it with a No CD crack and it runs. Unfortunately am i not aware how legal that is to use a cd crack even when you have bought the game (so you can´t really recommend that to Crossover buyers i guess).