It might have some conductivity, just nothing as effective as metals.
When we wanted a fibreglass vessel or lining which had some static dispersion because the contents might go pop with a spark, we'd specify carbon loading for the gelcoat. The surface presented to the contents was still resin rich but it was conductive enough to be classified by Hazards as not being able to produce a static build up. Having said that, I've a CF bike frame and I'd be staggered if that was conductive enough to pass !
Brian