IMHO... the answer is no.
There is no registration at the TH... or any clue of anyone's intentions.
Josh Lewis and I spent a night there. Two other male hikers got there before us. They were quite willing to share the lookout with us. There's a full sized bed to throw your sleeping bags on. There are also a couple of thick mats under that bed that can be moved out to sleep on.
If you don't want to share - take your own tent.
I don't know the squatter's rules... but I assume there's room to sleep 6 people on bed and floor in a pinch.