If you are NOT using EAD for work and you have
valid H1-B status, you can use AP to travel. Though it may be better to show H1-B on POE instead of AP. Just because you are having AP does not mean you have to use AP.
On the other hand if you are using EAD, you have to use AP even if you have valid H1-B visa.
* Use the info at your own risk. I am NOT a lawyer.