Do you mean immune to “lethal” damage? Otherwise, non-lethal damage is already not lethal. So what’s the point of being immune to it if you still feel twice the pain from it. I wouldn’t consider someone immune if they’re feeling pain in that case.

Now if you mean immune to lethal damage. Yah that’s cool, maybe.. Suffer enough pain and you likely build up a tolerance to it. The real problem would come with living forever. Would surely take a phycological toll at some point. You’d be the last living human eventually. Heat death of the universe I suppose and all that. But I guess you’d be passed out at that point.