You cannot get VAC'ed from a game that doesnt have VAC. I know this because at one time I tried to get an experimental Steam account to get restricted by the most games out there. (I got 7 VAC Bans and 43 Game Bans on said account). Game bans disable certain features within a certain game. VAC only works based on the game it was on (except the whole Source/GoldSrc group bans, which I consider as a single ban).
What you could be referring to could be account bans can be issued based on fraudulent activity on the account. I assume this would cause these sorts of bans.
Though I would typically need to write code that injects the game just right to trigger the anticheat; if this causes game bans this could make getting future bans a lot easier for said account