No Red Lyrium Dragon so no immortality. No Blighted corpses in the Fade for him to hop into and I'd be surprised if his current body survived the trip from the Inquisitor's Mark of the Fade.
Just seems to be a lot of speculation that no one in universe can actually confirm. When the whole thing about this guy was that we thought we killed him before and he didn't die, and we saw him die and (wait for it) he came back, you would think there would be a strict double-tap policy on him for the Inquistion. Yet, despite all these resources, time, and lives spent fighting him from getting into the Fade, we send him alive (assuming he will maybe die) into the place he's wanted to go the whole time.
Given that the Blight originated in the Black City in the Fade and no one except him and his Magisters have been there before, there's another pretty big assumption that this guy is finally dead after we just shot him through a rift. Just doesn't sit well with me that no one would be like "Umm, mister Inquisitor, what were you thinking? My brother/sister/uncle/lover just died to keep Corypheus from getting to the Black City and you may have just given him a free vacation there."