The narrator is definitely a character in this novel: we get first-person sections in both the first and last chapters, and he pops up periodically throughout Billy's travels through Germany. The narrator also spends most of his time telling us about Billy rather than about his own life, which is why we can call him peripheral: he's everywhere, but he's on the sidelines.
At the same time—remember, time is a tricksy hobbit in this novel—a lot of Billy's feelings and experiences seem to come from a third-person omniscient narrator who has complete access to all of his thoughts and feelings. This is not narration from the perspective of a person who is separate from the main character and making observations about his feelings.
In some ways, Billy's story reads like a thinly veiled and fictionalized version of the narrator's own life. The lines between the perspectives of the narrator's "I" and Billy Pilgrim's "he" are actually pretty blurred... much like the timeline.