Legally, Crossover/Wine is just another Win32 implementation.
It is not against the Steam EULA. There is nothing against alternate Win32/Win64 implementations, porting stacks, or emulation stacks in there at all.
Several game engine companies have stated that the Wine stack used in crossover is not against their EULA. Unity3D's statement on the Wine stack used in Crossover is that their clause against porting and emulation stacks are referring to mobile devices and consoles. Mac and Linux are considered Desktop platforms under the EULA and thus it is not a porting stack or emulation stack, just a compatibility stack.
As of anti-cheat:
The Wine API used by Crossover has never set of VAC systems at all. VAC uses a combination of variable out-of-range detection, and module blacklist detection. The API does not do anything against that.
VAC is very good at not false alarming, and has never been known to false-alarm on the Wine API used by Crossover.
Most other anti-cheat systems will only ever fail at the initialization stage where they don't result in bans. Under Steam's standards you cannot receive a VAC ban for all games for other anti-cheat systems.
Still, I would test that the game in question works on your machine with the anti-cheat system enabled before going and playing online with any game that has anti-cheat, just to be safe. (Generally there is a practice mode or tutorial you can do this in, if there isn't a single player campaign or local play against bots). This is also just about being polite. Make sure things are working before you play online because you don't want to bail on the other players if they are not.