Yes. Let the owner that you rent from know what you dining plan you would like. It would have to be added to the reservation at least 48 hours prior to the check in day. You will pay for the dining plan when you check in at the resort.
When you rent a DVC reservation from an owner you cannot add/arrange or drop anything pertaining to that reservation, so you need to discuss these details with the owner you are renting from if you wish for them to add DDP for you at least 48 hours before check-in day ( payable by you at check-in either by cash or credit card ). This is also the case for Magical Express as well (owner must arrange for you).