Pretty sure they want his death to be permanent, in DFFOO mobile game they have him proclaim how what he knows just stops after a certain point and how the others know more than he does. One of the best bits about this Lyse just wants to enjoy the time she has there but both of them fully accept his death for when they do return to their world. So I have to say it's conclusive he is dead if they want to heavily imply it in their other games(only reason don't think outright stated is it is a mobile game and kids could be playing they had a similar thing with Kuja and Vivi too).