I don't know if I understand your question, but will try to answer it as I think you are asking it - whether you can use your DDE card before it expires August 31 and after your AP expires on August 10.
You should be able to use it prior to the expiration date on the DDE. I have never been asked for my AP to prove that it is still good while I used the DDE card.
However, when you renew your DDE they request the number of your AP (I assume to check that it is still valid). I have been able to renew my DDE with an AP voucher, as long as I gave them the reservation number for our next trip (Again I assume, to check to see that it is valid).
So, I believe that you can use the DDE up until the expiration date, but am not certain that you would be allowed to renew it (as an AP holder) without a valid AP or AP voucher.