For those who are wondering, you can find out more information about the current promotion, which gives a free Disney Gift Card to guests booking select packages,
HERE.
To answer your question, without seeing the fine print on the hypothetical Free Dining offer, I can't say for 100% certain whether you could combine offers. However, I can tell you that I have never seen Disney allow two major offers to be combined. I think it is extremely unlikely that you would be allowed to use both the Gift Card promotion and a Free Dining promotion in the same trip.
Personally, if you are sure of the dates you want to travel, I would go ahead and book the Gift Card promo now. There is no guarantee that Free Dining will be offered this year, and the Gift Card is a sure thing.
Good luck with your planning.