Longish reply...
Please allow me to give a bit of background, before I delve into my full reply.
Our group now consists of seven people, three of whom (myself included) take turns DMing. Clearly, each of the three DM's have different styles and run different campaigns, and thus we all have more than one character to play, kept separate for each world. This may seem tedious or bizarre to some of you, but it keeps everything fresh from our perspective and allows the DM's a chance to re-charge on occasion.
One of the fellas who DM's loves to integrate very, VERY interesting NPCs and encourages unique and unusual character concepts. Some of his experiments have been truly brilliant, and have made the game more exciting than it otherwise would have been. When he DM's the world is never fraught with typical commoners, and PCs from the standard class and race list. His campaigns allow us to playtest feats, skills, spells and characters that me and the other DM likely wouldn't allow. In that respect (and others) it's a good thing.
Now, here's the negative side of this approach -- and the part I feel is relevant to your situation. About a year ago, this DM introduced an NPC very similar to the character concept you are proposing. This NPC appeared to be immortal, and while he wasn't a complainer he seemed to have no really useful skills or talents. After a short time, the group got very tired of having this character around...escpecially since he didn't fight much, couldn't cast spells, and never really helped in a significant manner. Like a previous poster mentioned, we took more damage than normal because our foes recognized that hitting this little freak didn't affect him to an appreciable degree. When the group was ambushed, he disappeared only to resurface to help rescue us; when a tough battle ensued he stayed out of the fray; and other than leading us past a few traps he was USELESS!! We did everything we could to get rid of this NPC, and eventually had to have an out of game talk with the DM because none of us were happy anymore. The DM enjoyed his creation, but none of us did.
All of that said, I implore you to really think long and hard before you introduce this character into your campaign -- in any capacity. Our entire group came to resent an NPC who never truly contributed to the group's efforts, couldn't help us overcome our challenges, and never seemed to be at risk of dying like we all were. There was a mountain of needless frustration, all caused by one person's desire to play a "cool" concept PC which left the rest of us in the lurch. I don't know your group or your DM, but I do know that the other players aren't going to like risking their creation's lives every encounter while you're having a blast roleplaying an immortal.
That's my two cents
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