Interesting subject! However, I don't remember reading anywhere that he may be a dead or unborn child, or even hint at that. In the novel, it is said that "when children died he went part of the way with them, so that they should not be frightened" but that's the only reference to dead children I could think of.
Peter Pan was never created as an immortal character, but a child who will not grow up and who wants to remain a boy forever, which is quite different. Eternal youth is not the same as eternal life. He is prepared for death, as we see in the scene on Marooners' Rock and during the fight with Hook, and death does not scare him.
In the play, Barrie refers to the "riddle of his being", which I take to mean his refusal to grow up and accept adulthood (and fear of it). Indeed, "if he could get the hang of the thing, his cry might become 'To live would be an awfully big adventure!'."
In other words, I do believe Peter Pan can die... These are just my own thoughts on the subject, but others may have other ideas!