If you are going in a few weeks, there is a good chance you will already have trouble getting into the more popular places if that is where you want to eat. I have seen countless amounts of people get turned away from TS restuarants, and during off times too. I have also seen people get lucky.
Free dining can make it very difficult to get into table service restaurants. If you aren't picky at all about where you eat, and don't mind if you can't get into any table service restaurants and are stuck eating counter service, you will be okay- you certainly won't starve. Most of the time, I'm guessing you can call that morning and pick up a table service somewhere at Epcot, if you don't care where or what time you eat. As far as the MK, last December there was nothing available for dinner AT ALL for the 1st night we were going to be there...I tried for almost 2 months before our trip to pick up an ADR anywhere. (I did not book on the opening ADR date, because I didn't know how early our flight was going to get in, I started trying once I knew we would be in time for dinner). I finally did find something, and when we got to the parks, there definitely was that sign up that said there were no table service ADRs anywhere that day. I have seen that sign several times at MK, and I have called the day before or morning of and been told that there was nothing available when we have changed our park plans.
If I were you, I would go ahead and make at least a couple ADRs. You can always cancel them if you find there are other things you would rather do that day.