Lisa,
I think it depends on what time you board.
We boarded very early and went directly to Parrot Cay for lunch - lots of open tables as many other early boarders were busy getting reservations for Palo or the Spa. You would have had little problem finding room for a large party (although you may have ended up at two tables close together, depending on how large).
By the time we left, Parrot Cay was quite full and you'd have had a problem finding a table - but they had only just started to direct people towards Topsiders - which doesn't have a lot of big tables, but you'd have been able to sit close.
A little later, and Topsiders is quite full, Parrot Cay has cleared its first rush. And shortly after that, lunch dining stops and you'll be having pizza or a burger.
