I just came back from China using AP. I only ted one original copy of AP, no other things except the passport. The officer spent half minute to stamp my AP, wrote I-94 and attached to my passport, then gave back to me everything.
Nowadays, more and more people use AP and they won't question anymore for this document, and I didn't see any other people before me were questioned when they were using AP. But I guess no hurt to prepare everything that proves your legal status in case any officer has questions.