Yes. I’ve actually done this on a west-flying jet; it stayed just before sunset for 8 hours as we chased the sun. Another time the my plane had really good tailwinds on one leg of the journey and we got to celebrate new year’s twice during the flight.
Chasing the sun, it would be the same time until you hit the international date line, at which point it would suddenly be the next day at the same time.
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