I've never done that with my points, or with old navy, but overall, the answer is...it's up to Old Navy. If they allow "earnings" on sales using gift certificates then you would; I've done it through sunshinerewards with shoebuy and famous footwear, in the exact way you've described! But I try to never *count* on earning when using a gift certificate, because it's not something that all merchants will allow.
All that said, giftcertificates.com has changed in the last few months, and they have all sorts of fees that cut down the "earnings" you're getting. They even charge for email delivery now, though it's not totally clear that you will be charged until, well, you have been. And it seems their customer service knows it's a problem, knows that they have changed, and they just don't care. Though I used to order through gc.com, I won't anymore unless I absolutely have to (and that scenario hasn't happened yet).