The narrator might believe the details of "Rip Van Winkle," but the author does not and does not intend for his readers to find the story believable. Washington Irving is a satirist, and the primary focus of his satire is early America, especially the Puritans and early superstitions.
Because Irving created quirky, stereotypical narrators like Dietrich Knickerbocker and Geoffrey Crayon, I think that the narrators themselves are part of the mockery. So, it would make more sense for "Rip's" narrator to believe the tale he is telling so that Irving can make fun of not only the stereotypes in his story (the henpecked, lazy husband and the nagging wife) but also the fable weavers of early American legends and the people who are naive and superstitious enough to believe the stories as "Gospel truth."
I think that the narrator of the story probably does not actually believe the story. The narrator states that he does believe the stories to be true (in the note at the end of the story) but I don't think he means it.
I think, first of all, that the narrator is trying to overdo it when he says he believes the story. He talks about it being an "absolute truth" and says that no one could possibly disbelieve it. I think that the author of the story means for the narrator to sound like he's trying to hard to convince people that the story is true.