I think its less a question of the technical feasibility, and more of an issue that we, as users, don't want more closed-source blobs in our kernels. Meanwhile, the publishers insist that they can't open-source their anti-cheat code; Their idea being that if we know what's in it, it will be easier to bypass.
Basically, one distro or a few(at most) may get anti-cheat integrated one day(like, say, SteamOS), but it will likely never be in your standard Linux kernel.
They could go the route of kernel modules, I would think, but for whatever reason, we're still having this conversation.