Maybe this is just for the game play sake, but my question is why. If you don't want an NPC being killed or attacked by the player, essential and invulnerable is enough. Why make a character appearing in flesh but in fact a "Ghost", only to let him not be affected by detect life?
This makes me think, what if Gelebor is actually neither a living person nor a dead one? What if he is, or becomes, actually an Avatar of Auriel, that waited the Dragonborn to come and fetch his bow?
Gelebor used to tell the Dragonborn that about people come to fetch Auriel's Bow:
For the thousands of years I've served as the Chantry;s sentinel, there hasn't been a single visitor here for any other reason. They requested Auriel's Bow, and I request their assistance. It's been repeated so many times, I can't imagine it any other way.
It seems for thousands of years Auriel's Bow had been a common guest to the Chantry. And the first question arise in my head was: Why would Auriel's Bow appear again and again and again in an almost dead Chantry of Falmer instead of those Churches of Summerset Isles? There used to be records that this bow was always in a state of missing. I don't think being kept in Summerset Isles would be considered as "missing", so was it being kept just in this Chantry of the Falmer? Artifacts have their own minds and ideas, but is the savage north with so little worshippers of Auriel really that attractive to his weapon? And this weapon was not used by its priests and paladins, but all others who came to borrow it?
However, if Gelebor is in fact an avatar, then the answer is very simple: Auriel had sent his bow out to the ones who really needed it for the good of his followers so many times in thousands of years, not only in the Chantry of Snow Elves, but also other chantries for him across the whole Tamriel. So Auriel's Bow appeared from place to place to help heroes defeated their enemies, but every time directly from the hand of the god at the start. If the artifact was missing, it was right in the hands of its master and not in Mundus.
And, the avatar theory also explains why Gelebor declared himself living "thousands of years", also his ablility to bless the elven arrows.
If Gelebor is really an avatar, then his conflict with his brother Vyrthur would become a little more interesting, because it is a conflict between brothers, just like the war between Auriel and Lorkhan right before the Convention. Though not mentioned in myth itself, we do know the enantimorph contains the twins of dragon and serpent, time and space. Of course, it is only similar, because Vyrthur had lost his soul before the Dragonborn intervened. But the relation of Gelebor-Vyrthur-Dragonborn is also similar to that of Auriel-Lorkhan-Trinimac, as Vyrthur is the Arch-Curate aka the King, and Gelebor the Rebel to move into the Chantry, and Dragonborn the Thane that killed the King and Observed/fixed the conflict result.
I do think meeting an avatar of an Aedra-Magne-Ge who is claimed by the Thalmor their Lord would be interesting, as Gelebor seems not as a racist to extreme as I thought Auriel should be.