Yes you can. If you are purchasing a cash package, it is like any other resort.
If you are a DVC member and staying on points or renting points from a DVC member, you can add the dining plan. You just have to add it at least 48 hours before you arrive (if you are renting points, the member you are renting from must add it to your reservation for you). You pay for the dining plan when you check in and there is no ticket requirement to get the plan. Otherwise it is the same as the normal package (cost, what you get, the need to buy it for everyone in the room and for all nights).