No, the free dining offers are not available to DVC members booking reservations through DVC Member Services.
Free dining is available only with a very specific type of reservation - a package reservation of at least 3 nights and no more than 14 nights (21 nights on the British offers), including at least 2 day park tickets for each guest age 3 or over. The reservation must be made directly through Disney CRO (Central Reservations) by the guest, or by a travel agent on the guest's behalf.
DVC Members can book free dining packages through CRO, like anyone else can, but they cannot get free dining on points reservations or on cash reservations made through Member Services. They may, of course, purchase any of the three Disney dining plans with a DVC reservation. so you'd have to decide if you want to use DVC points, or if you want free dining.