You can. You just can't stack discounts, so you have to choose one - AP or DP. Even without a reduced room rate, the AP is itself a discounted park ticket. If they'd let me get the DP when I went room-only with an AP, I would, but I don't know if they'll ever feel the need to do that. The DP is a marketing tool, after all, and AP room rates already get many APers back.......
Check into the DDE card, though. Depending on your eating habits, that might be even better than teh DP.