Thanks Amazon for your responses.
I didn't have a valid H1-B stamp in my passport while re-entering; so I ended up using my AP. I did have long discussions with my lawyer before doing this though.
For the benefit of anyone else having this question: Merely re-entering the US based on an AP does not invalidate one's H1-B status. In fact, even after re-entering on an AP, one's H1-B visa can still be renewed (if all the other criteria allow for it). The only practical thing to know about entering on an AP is that CBP sends you for "additional processing" at the airport, and there is a wait for it. In my case, I wasn't really asked any questions or anything, but had to wait my turn (for about an hour) on a day that was particularly busy for the CBP officers.