You can on both counts. Here's how I know.
When the AP discounts for Aug/Sept were released, I went to the WDW website, to the Passholder section to see what the rates were like during the same
free dining period that our trip is booked. The promo page gave me two options: room-only or room+dining (no tickets). Here are the prices I got:
**The same room I'm getting at CSR at $99/night, total of $780 for 7 nights.
**CSR, 7 nights including
DDP, $1385. That's $780 (room) + DDP for 2A/1C (~$605/7 nights) = $1385. If I were having to pay rack rate for the room with the DDP, the total would have been more than $300 more.
So, I know *for sure* that you can have an AP, book a room with the AP discount and add the DDP to it.
I had a similar calculation for WL. I had priced the free dining package there for a Woods View BB room and came up with $23XX for 7 nights. The AP package I priced was $2054 (room + dining).
PS - My free dining package at CSR is $1391, so only $6 more, and I'll get the 1-day tickets that I can use to renew my AP next time.