Unfortunately, it's pretty conclusive that Papalymo is gone forever - his aether was consumed to create the Dalamud-like coccoon used to seal Shinyru temporarily, and once that shattered, the last lingering traces of his life disappeared forever (as shown by the fake Sharalyan Circle of Knowing tattoo Lyse was wearing also disappeared, as that too was connected to his aether).

Sadly, I think he's not coming back, despite how affected I was at seeing his demise, along with the revelation about 'Yda' (Papalymo and Yda (the real one) were the first two npcs I ever saw in FFXIV way back in version 1.0 so I was really saddened at not just his death, but also discovering that Yda has been long dead and it was just her sister masquerading as her all along, at least since the Calamity.).