They don't show up and race at track events because their cars are set up to run on the STREET. Completely different chassis and suspension set ups. If they just showed up at a track event where it was prepped, they would have such severe tire shake the car would come apart.

Also, watching the show, I don't recall seeing and NHRA decals, hats, shirts, etc, that would lead me to think they were involved with the NHRA.