I meant - you can go to India with an AP. Try to stamp H1. And regardless of outcome of stamping you can enter on AP and still work on approved H1B.
The denial in India of H1B stamping is just denial of a visa. That doesn't invalidate the H1B work authorization. The reason for this apparent disconnect is because of the fact that visas are given by DoS whereas work authorization H1B is under USCIS.
My understanding is that if you enter on AP - then you automatically acquire status by using your H1B. But you may want to confirm with your company lawyer.