I just came back from China last week, using AP to enter the state in Chicago. The procedure was extremely simple. I just gave the officer my AP (two copies) and shew my passport.
After looking at my AP, he told me that a special stamp was needed to stamp on my I-94 and passport. He got it from another officer in next window.
I was not asked to go to any other room. It took me no more than 3 minutes. I did bring my driver licience, credit card and I-485 with me. But, they were not asked for by the officer.
Good luck!
Good luck to you.