I would give it a try. Also, some restaurants, like T-Rex, will show not available on Disney website system, but if you call the restaurant directly, they will set up a reservation for you.
Also, if your party is very large (like 9 or more) you have to call the place directly. For example, Tutto Italia can't accept online reservations of too high a party count. I called Disney reservation center, and a CM confirmed that I had to call directly, gave me the direct number, and I got a reservation for our large party. That Tutto Italia dinner was one of the highlights, by the way.