Just FYI - we just got back a couple weeks ago. Our trip was a gift from my in laws (what a blessing!!) but my MinL made ZERO ADR's. As a family of four (or three and a highchair) here is where we were able to walk up to, seat immediately and dine:
Breakfast with Mickey, Lilo, Stitch and Pluto and Ohana at the Polynesian
Lunch at Hollywood and Vine (way too young for these kids!) w/ Playhouse Disney
Breakfast with Mary Poppins, Pooh, Alice in Wonderland, etc. at 1900 Park Fare at the Grand Floridian
Dinner with Prince Charming, Cinderella, Wicked Stepmother, & Stepsisters at 1900 Park Fare at the Grand Floridian
Lunch at The Living Seas? Rest. in Epcot
Breakfast at Kohna at the Polynesian
Dinner at Tusker House in Animal Kingdom
I list all of this only to say that if you are a small party (4 or less) there is a good chance you can eat almost anywhere, if you are a little lucky and show up to the right place at the right time!
Hope they have a great time!