Yes, they would have to be closed once they get to 1000 posts for that thread. It's too frustrating to go through more posts than that when searching. Although, it's easy enough to do a "search" within the thread and/or forum to find what you are looking for.
I'll bring the subject up to the Team regarding making check in threads a sticky thread. Once they get to the 1000 post, we can unsticky them and sticky the new thread.