I think it depends on the restaurant. You may end up waiting a bit (i.e., 30 min or less), but you should be OK at most places. Last year, we had breakfast at Kona, Spoodles, and (more than once!) the Yacht Club Galley (now the Captain's Grille) without ADRs.
However, if you have something you specifically want to eat, you may want to make an ADR so you know you'll get in.