Spots are always held open for onboard booking. Check as soon as you board.
I don't think they actually pack the tables at any given time. It adds to the illusion of luxury to have vacant tables, leading to more attention from the serving staff. And a quieter ambiance all around.Given the anxiety often expressed here about trying to snag a Palo reservation, I was amazed on our Alaska sailing to see a great number of empty tables even though reservations appeared limited or non-existent online. Perhaps the different Alaska vibe has some effect on bookings.