I hate to be the bearer of bad tidings here, but we just got back from the world on Monday. The parks were not any busier than usual, but the restaurants were mobbed. I'm sure this is a direct result of the dining plan.
We had ADRs at Liberty Tree for lunch last Thursday at an odd hour (2:45) when you would expect it to be not too busy, but they were turning people without ADRs away. (As a matter of fact, EVERY restaurant we went to last week was turning walk-ins away). We were on the dining plan, and had made all our reservations months before, but if we hadn't, we wouldn't have gotten in anywhere.
I reply not to be negative, but to encourage you to make ADRs somewhere else as a backup plan. I'm afraid that the days of walk-in dining at table service restaurants are over.