Had to log in here to tell the truth...
Getting vac banned does not cause you to be unable to play any other game beside the one game that you got banned in. I believe that was how it worked for a while a long time ago, but for a long time now you've been able to play steam/valve protected games even if you have a vac ban.
Source - I have 2 vac bans on my main account and can still play TF2 and other steam related games.