Absolutely no reason why you can't. But make sure the divider goes all the way to the bottom board and all the way up to the cover, then block the entrance to side you don't want them to use.
Iddee is right, if they get to the other side before you are ready to pull the divider, they will build whatever they want. So, to that end, it's not a bad idea to leave four or five frames in the other side, just in case there is a way for them to get in there that you didn't know about.