If you ingest human hair, will it kill you?

The hair itself is not much more than protein. It might be a bit dirty, depending on where it has been, but it won't cause a chemical interaction that would be fatal. The quantity you ingest may indicate other outcomes. If you could manage to swallow enough, a large amount of hair could block your digestive tract (hair cannot be digested) and require a stomach pumping. In that sense, it could kill you if left untreated. Though you would be in such pain that you'd seek treatment right away.