carbon fiber is generally the fibers encased in resin… so I think you should be ok, but you should make sure there’s no pvc in it before you do anything.
Odds are it won’t do much at all. The GF can’t cut or burn the Carbon Fibers, all it can do is cook off the adhesive. So if the surface of the CF is shiny, you might end up seeing a ghost-like image after engraving. But you’re not going to be able to cut any depth like a normal engrave would.
Also, you have to be careful with things you put in the GF. The adhesives can be made from chemicals that breakdown in to highly toxic or corrosive gasses. Low odds of this for Carbon Fiber, but not zero odds.
Most resins, the stuff holding the carbon fibers together, are considered toxic to laser cut. Unless you can be very certain of the MSDS on that piece I’d avoid.