I've done this several times with no problem. In fact I just got back from WDW May 13th and used the DDP for my meal at Spoodles, while using my DDE for the Sangria. Like the previous poster said however, they will automatically add an 18% tip to anything you order in addition to the DDP.
The only time I've ever had a problem doing it was at San Angel Inn Sept '05. I don't like San Angel Inn, but my D-I-L wanted to eat there. I didn't want to waste a TS credit, so decided to let my son and D-I-L use their DDP, while I used my DDE card to order just a drink and cheese fundido for my meal. They refused to let me use my DDE telling me we all had to use the DDP. We even had the waiter call the manager over, but they still wouldn't let me order separate. She said they would only accept one discount/table and both the DDE and the DDP were considered discounts. However, that same trip I used it other places to order drinks or even a separate meal and never had a problem.