Sure you can, but at some times of the year a PS is required. Disney calls them PS (priority seating) instead of reservations.
What time of the year are you going? I know they are a couple of restaurants that regardless of when you go, you're going to need a PS. Cindy's restaurant in the castle at the MK is one and I believe Chef Mickey's is the other. Both those restaurants book quickly and chance of walk-in is slim to none. I've heard it done at Chef Mickey's every now and then, but I have never heard it done at CINDERELLA'S ROYAL TABLE.