Hello Dominic7
Yes, the Friends Day Pass for Youth for 1st class is valid for the Gotthard Panorama Express.
https://www.sbb.ch/en/tickets-offers/tickets/day-passes/friends-day-pass-youth.html
However, the supplement (seat reservation for the train) is to be paid by each member of your travel group.
https://www.sbb.ch/en/tickets-offers/tickets/day-passes/friends-day-pass-youth.html
Alternatively, you could take the IR26 or IR46 trains, also known as Treno Gottardo, which both take the same route from Flüelen to Bellinzona as the GoPEX yet are regular services; thus, a Friends Day Pass for Youth for 2nd class would be sufficient and no seat reservation is needed.
Kind regards,
Roland