No, you can not reserve a table, in the strictest definition, but I was just on the Serenity in Jan - Feb, with an almost full ship, and we had the same table set up for 9 every evening after our group "leader" spoke with Leo the first day. The table was basically ours as we showed up at 7:30 every evening we were there and not at a specialty. Leo was also reminded before the nights we were going to the specialties so that the waiters did not need to set up "our" table. It certainly wouldn't hurt to speak with the maitre'd the first day and ask if this is possible.
Patty