It's very likely that you will not make it to the ship until 2pm. You since you are on a 7 night cruise you have a good chance of making Palo ressies (you may have to be flexible). I'm not sure how late the lunches go to - you may want to stop in at Parrot Cay or Topsiders for a bite to eat first.
Even if you don't make it to lunch, up on deck 9 theres there is Pluto's (burgers/brats/hot dogs, nachos, chicken strips), Pinnochio's (Pizza - which is very good - especially the daily special) and Scoops (Ice Cream, chocolate chip cookies and fruit). These are open until 3 on embarkation day and then shut down for the manditory safety drill. They reopen after the drill.
Have fun.