How does the narrator's role as protagonist affect the impact of the story, "An Occurrence at Owl Creek Bridge"?

That's a difficult question to answer, because the narrator is not necessarily the protagonist. In fact, through most of the story, the two are definitely not the same: the protagonist is spoken of as "he," and there's no sense that there is a distancing by a narrator protagonist. Only the self-consciousness of the final paragraphs might indicate that they are the same, and even there it is doubtful. If you read those paragraphs that way, I'd say that the narrator's role as protagonist affects the story by underscoring his distance from himself: it indicates that he's dead and distant from life.