I got a $10 gift card from TDS when I pre-ordered Treasure Planet and bought other merchandise as well. When I went back to use the gift card toward my DD purchase (I had called first and spoken with a manager), the manager on duty checked the back of the card (for codes, maybe?), saying that some gift cards are eligible for DD purchases and others are not. I was prepared to stand my ground, armed with the name of the manager I had spoken to a few days earlier, but apparently the card was the "right kind", as it was scanned in on the register successfully, and reduced my total balance due for the DDs.
So that might be another question to ask when you call your local DS to ask about this.