It likely would put a damper on a positive working relationship. However, having keeping tabs on the avatar of your religion's biggest bad guy would make a perfectly legitimate reason to tag along.
Or, alternatively, the glowing eyes may also mean that the librarian is about to get possessed or hijacked by the Light Dragon, in which case we get a 3-way dragon fight and (if he retains any memory of it once it is over) Erin has an existential crisis as he'll have personally seen the thing he refuses to believe exists.