Cinematography is a form of visual communication, so becoming steeped in literature and narrative can't hurt as a filmmaker. It also doesn't hurt to know how to express yourself in writing -- not just in the film industry but in life in general.
But obviously the benefits to one's career as a cinematographer are subtle at best.
In general, I think it's good to have some knowledge in areas outside of filmmaking, if only to make you a well-rounded artist and individual. So I've never been completely convinced that a BA in filmmaking was a good idea for an 18-to-22-year-old; it's a bit early to specialize.