Perhaps this can fit in the meta chatroom, but I feel like it's something that's answerable by mods (feel free to move elsewhere if it's not appropriate here).
If a user is suspended on the main site, does the suspension translate to the site chatrooms of that specific site? Perhaps there are exceptions (I'm thinking that if an only chat suspension exists, maybe there is also an only site suspension), but in general (put more directly) if I get suspended can I still use the chatrooms (on that specific site)?