There is a
DVC forum for your future DVC questions.
Yes you can take advantage of free dining.
However, you can only book this offer on cash (same as you do now) you cannot book your hotel with points and receive free dining. Since DVC is already billed as a discount, you cannot "double dip" and get the discount for booking with points as well as the free dining discount.
DVC isn't a discount program, it's a timeshare. So, while it is true that members staying on points aren't eligible for free dining, 4/3, pin codes, etc, it doesn't really have anything to do with double-dipping.
Those promotions come from the WDTC, the division of Disney that books the resorts, and are meant to get bodies into the resorts. DVC is an ownership situation - we own part of our home resort. As such, we don't give a dime to WDTC, so there's no reason whatsoever for them to give us hundreds of dollars of free food, or any other promotional discounts.
Not that I consider that a hardship.

When you compare the cost of staying in a deluxe resort on a cash reservation, even with 4/3 or free dining, to my lodging costs as a member, I'm coming out way ahead. And I get that deal anytime I want to go, I don't have to hang around waiting for a code.
Is DVC the cheapest way to stay at Disney? No way. If you're comparing free dining at a value resort to DVC, sure, the value deal will be cheaper. But for those of us who'd rather stay deluxe, it's a terrific deal.