No, you cannot. A points rental has nothing to do directly with Disney. To get free dining, you must book with Disney and have a package with a full price room + a minimum of a two-day ticket for everyone in your party.
If you rent points from an individual, you can add a paid dining plan without the purchase of tickets, though.
When you stay at DVC in any other way (using points as an owner, renting points from an owner, exchanging in through RCI, etc.) besides paying full rack rate for the room, the only way to get the dining plan is to pay for it.
I can't imagine ANY circumstance where it would actually be cheaper to pay full rack rate on a DVC unit and get free dining than it would be to just pay for the dining plan.