My serious comment - yes you can!

No to nepal but I used my Ap to travel to Netherlands. Upon returning just the same procedure, 2nd inspection room, wait for 2 -10 mins depending on the rush hour and the officer stamps paroled on both your passport and Travel document.

I have AP as well but just doesn’t have courage to go Nepal.

Not to Nepal, but I traveled to South East Asia on August, my Point of Entry was SFO, parole stamped without hassle , 1 minute on initial inspection desk, 5 min wait on secondary inspection room, 30 sec interaction with secondary cbp officer.