No, they don't set aside any tables for walk-ups. Many restaurants will just turn you away if they're fully booked for the rest of that meal, and most theme-park and character meals are fully booked every day. This can even happen with the resort restaurants. I called one Saturday evening around 4 for an ADR for that evening, and was told that every single TS restaurant in the MK and the monorail resorts was not taking ADRs or walk-ups for the rest of the night.
As the PP said, some people have success arriving right when the restaurant opens, but obviously that's only going to work for a handful of people at any given meal.
If you want to be sure of getting in to a TS restaurant, you need ADRs. If you're willing to be very flexible as to time and location, or would be happy with CS if you can't get into a TS place, then you'll be fine without them.