It depends what you're asking.
Do you get a discount on the purchase of the DDE if you buy the
DDP? No (ditto for the reverse).
Do you get the DDE discount piled on your DDP purchases? No, since once you order using the DDP, there's no additional cost for the appetizer-entree-dessert-nonalcoholic beverage.
Can you use the DDE discount on whatever you order that's not covered by your DDP, like an extra dessert or entree or alcoholic beverage? YES.