According to the AP website, AP holders only had early morning entry through September 13th. I was looking this morning to see if the promotion had been extended, but it doesn't look like it.
Err, you mean like if you AP expires on 1/1/13, can you still get into DLR or DCA on 1/2/13? In this case, no, the expiration date on the pass is the last date you can use it to enter into a park. I think you can still renew it at the AP renewal rate for up to 30-days after the expiration date (but the start date will be back-dated to the original expiration date).