As others have said it is ultimately up to the POE officers. My wife and I got married last year and were concerned about a family cruise to the Bahamas since the cruise line was very vague. My wife and daughter both had their AP and we had no issues with customs returing to USA. Customs did pull the three of us aside into another room, reviewed their AP documents (took about 20 minutes) and then thanked us and let us on our way. To be safe we had copies of every document we could think of but the only thing they asked us for was their AP card/papers. Again this was our experience and I'm not sure how it may be for you or anyone else.
DHG got a reaction from Hemutian in Advance Parole, Any problems returning to USA?