I used my AP paper to enter back into US in Dec 2013. At the Dallas Immigration, I was asked to wait in the room along with lot of other immigrants. I sat in a crowded room for 30 mins when my name was finally called. I went to the officer and he handed me my passport. "Thank you and have a good day" was all he said. I guess this wait was because of the change in my status as all the previous entries were on F1 student visa status.
To sum it up, you should be fine traveling on AP. That's what AP is for anyways! Hope that helps. Best wishes!