Can’t speak to anti-cheat, but I’ve run a Windows 11 VM with GPU passthrough on Proxmox. I got basically identical performance from the hardware, considering the reduced ram/cpu count in the VM. USB port passthrough was glitchy though. I didn’t spend too much time messing with it but it definitely was functional. Battlenet (World of Warcraft, Overwatch, etc…) worked fine. I don’t recall any game that didn’t run but, again, I didn’t do too much.
This is what we call a “bad idea”.