You could get lucky and get in like we did. We showed up for breakfast about 10:15 and put our name in. We were handed a pager, started to walk away from the podium, and we were beeped, LOL! We were seated right away.
If you are sure you want to eat there I would book a PS just to be safe, but if you end up trying at the last minute with no PS, you "could" get lucky. Good luck!