Yes, MDR Anytime Dining reservations can be made onboard. There are Specialty Dining podiums near the Pinnacle Grill and Spa entrance on embarkation afternoon. That is also where MDR reservations can be made. However, they allow no more than 50% of the tables to be reserved. Some ships allow you to book for the whole cruise and some ships allow booking only 3 days in advance.
How long the non-reservation line is varies by when you want to dine.