Yes, you can purchase the
DDP with an AP with no additional ticket purchase. You have to purchase a ticketless AP package with dining. I believe you have to be using an AP rate for the room or paying rack rate for the room, but that part is a little fuzzy to me. I've seen a handful of reports that suggested otherwise, but most say that.
You cannot get free dining, however, without buying the minimum tickets required for any free dining offer.