I suppose this question greatly depends on your definition of existence. If, for instance, we are speaking of existence in a strictly literary sense, then yes, Peter Pan really existed in the story itself.
If we are being more pragmatic, however, and asking if Pan existed in "real life," then no, he did not. H.M. Barrie's imagination was the primary dwelling place of Peter Pan and his related characters. The only real opportunity to see Neverland today exists at, you guessed it, Disney World.
All good literary characters are based upon sketches drawn from actual, living and breathing humans. Peter Pan and Wendy, John, Michael, and the lost boys are no different. However, Barrie's interpretation of these characters makes them completely fictional rather than biographical.