Do you have to make advanced reservations? I'm not sure how all of this works. We're about three weeks away from our trip, are we going to have a hard time finding places to eat without reservations?
Ask yourself a handful of questions:
Do you want to eat at table service meals?
Do you like to eat at "normal" meal times?
Do you mind traveling to a restaurant if needed?
Are there any restaurants you really want to try?
It comes down to this... if you want to eat at table service during normal meal times OR if you want to go someplace in particular then you need to make reservations.
If you don't care if you eat table service, where you eat, or if you have to travel to another park or resort to find a place, then you might be okay without.
If you don't have ADRs then there is a good chance you will not get into the restaurants you want. If there is anything open, they will be less popular places and you may have to go elsewhere to get a place that is open. You may even have to settle for counter service depending on the time or situation.
I would sit down, look at menus, and try to book a few things.