Yes, the Dining Plan may be added to DVC reservations. The member will need to do that for you at least 3 days prior to arrival. DME can also be added by the member.
It may depend on when you are going. DVC has stated that the dining plan will be paid for in full when it is added to the reservation in the near future. If you rent a reservation from a member, they will have to pay for the dining plan unless you give them a credit card or pay for the plan in full when you decide to add it to the reservation. You cannot add it when you arrive and must add it at least 48-72 hours ahead of time.
So it may depend on the member and how they want to handle it.