Jeanie is correct. Formal dining rooms closed until dinner, serving crew get that morning/afternoon "off" typically, but all pool area service (hot dogs, hamburgers), as well as the buffet, etc. all open. Plenty to eat if you board early.
I checked in April and the dining room was indeed open for lunch and we saw people eating there. We were told it was a "reserved" event, what ever that meant. I think it was back to back guests only. I heard later from people we met that if you asked to sit there, they would let you.
I was checking through the Princess site and found a section on 1st day dining. It says that they do offer dining room lunch on the day of embarkation. Here is the link to what I read, maybe you can find other helpful info