In the ' early ' days of composites for structural use on airplanes ( other than feathers- flaperons, etc ) there was significant discussion as to conductivity of carbon " dust " from machining and cutting of composite structure. A lot of trimming and cutting was done with abrasive ( brazed industrial diamonds on high speed cutters ) really a grinding process. Abrasive high pressure water jets were /are also used.
Anyhow to settle the question- a simple test method was used . A half/pound or so of ' carbon composite grindings' was put into a small plastic box over 90 percent full. As I recall, the box was an inch or so deep and about and size of a binder. On opposite sides an simple wire probe was inserted and sealed. resistance between the two probes was measured as the box was shaken - no reading indicating no conductivity. My very ancient recollection seems to be that low to moderate voltages ( dc ? ) were also applied. Results indicated zip current.. IMO not to surprising when one considers the fact that tdo establish a conductive path with carbon ' strings' covered with some epoxy- several thousand would have to line up end to end in close contact to pass any current. So much for composite ' dust ' conductivity.