Now you have thrown NRT and BKK to the mix. That is very likely to change the calculations. What is you actual proposed itinerary?
If you are simply doing a BKK-HKG-ORD then yes adding a NYC segment after a stop over will not be a problem.
OP might even go to SJU.
I had a BKK-HKG-SFO (stopover for months)-MIA-SJU once on a First Class milesaaver.