They would still be able to post but their posts wouldn't bump the thread to the front page. And requiring to post in the ANN thread is already against the rules.
Although I still prefer stompix's idea of having to spend merits to bump a thread. This would cost abusers a lot more than just getting a merited account and using it for unlimited bumps.
Alternatively, we give the owner of the thread a bump button which they can do at any point allowing them to bump their threads strategically or when they are online. Don't allow posts to bump threads anymore. Only allow the button to appear every 24 hours.
I wonder if those "ICO managers" or whatever they're called (the ones who create ANN threads on behalf of various shitcoins) could abuse this.
E.g. wait for your competitor to bump their thread and then bump 50 of your threads immediately, knowing that the competitor can't do anything about it for the next 24h.
Come to think of it, just create 500 dummy ICOs and bump anyone you don't like off the front page. Much harder to do that when there is a more tangible cost, like a merit.