It depends on how their ban system works. Id say no, its unlikely to affect other accounts because a ban will probably just be a ban for the specific account in question.

However, they may be able to ban your IP meaning any account connecting from your IP address will no longer be able to join a Valve multiplayer game but I have no idea if Valve operate this kind of ban.

There are 2 types of bans you may encounter when playing a a Valve game. The first will prompt the message "SteamID is Banned", this is a ban implemented by the server owner and does not affect any other server. Any server owner can ban you for any reason from their server. The second is an actual Valve ban and will prompt the message "Your connection to this secure server has been rejected. Because of past cheating violations, you have been banned from playing on all secure servers" and is as serious as it sounds, your account has been banned from all servers running the VAC client.