Would benzene be able to conduct electricity?

I poked around a little and found a reference to hydrocarbons in general. They are very good insulators.

 

No, it is not.

In graphite, the [itex]\pi[/itex]-electrons are delocalized over the entire plane of C-atoms, while in a benzene molecule they are only delocalized within the molecule (ring). There is no mechanism in benzene to allow the electrons to hop from one molecule to another. This is similar to the fact that in-plane delocalization in graphite means you can conduct well only along a single plane but not from one plane to the next.