I don't see why not? The game database is already connected somewhat to the website due to it banning you from the game when you're banned on the site, so that part's already done. All they need is a function so that as soon as someone submits the ban on the site, it would send a command to the game to kick.
Overall a good idea. If someone knows they've been banned on the site, it may lead them to a "F* this" mentality in game