Hi Celsius,
yes Counterstrike works on Linux, using WineX. I tried it myself, so im sure about that, however you will NOT be able to play online (Internet) games, because Valve's anticheat does not work properly yet on Linux...therefore you will be thrown out of the game, and possibly banned as a cheater

Valve and Transgaming, Inc. are working on a solution that will most likely be implemented in future WineX releases.
Other games that work (with WineX), tested by me, are:
Soldier of Fortune 2
Quake 3
RTCW
The trick is to either run the game executable from a Windows partition (game already installed in Windows), or run the setup.exe from the game CD and install it on the virtual Windows drive that WineX creates.