I don't think anyone knows for sure - but we can speculate and a) assume its done on the serverside and b) connects to a website (api.garrysmod.com) and checks if you are on the blacklist.
If it does connect to the website I would be curious what would happen if the website goes down. I have a hunch that once you are 'banned' you client is somehow modified so you don't keep on querying the server (re-installing GMod should reset it).
Edit:
Basically a 'bypass' for the ban is near impossible.