In the days of CSHP, they used to, but not so much anymore.
1. The "file" to be downloaded would have to change md5 or something every time, generating some form of random file information, so it would be different each time, other wise, once downloaded from a server, a program could concieveably hack it for next time. It might even be softice hackable still, though I'm sure they'd hook before having to do that. Most cheats now are facilitated by exe, and are completely outside of the game.
New DX and GL hooks are making many aspects of cheating easier to make, and harder to detect.
2. If that file is randomly different on each connection, it would have to purge itself every so often, probably requiring some harddrive rape by the running mutator, meaning when you are playing. Otherwise, your cache folder could get big quick.
For the most part, the "basic kiddie cheats" are already taken care of with decent efficiency. The reason cheat protection starts getting complicated, or hardware intensive, is from the nasty cheats. Currently, a dumbed down anti-tcc is good about not raping your game performance, and keeping nasty cheats out. It can be set to rape your harddrive, and be more secure for the nasty cheats, but mostly, it stays a direct ratio.
That idea might work for more complex cheats, but again, implementation has a couple drawbacks off the drawing board.