Yes, it shows. It also pops up if you run the license plate and one of the registered owners has a permit. WA OR ID are the states that I know of that it works that way.
That is a bit of a concern, so now I have to worry about my wife or worse kids getting hassled for driving one of our cars because I carry? That is crap. Tie it to my license all you want, but really, every one of my vehicles is now flagged as armed, how are they going to manage that given I never provided any of my vehicle information and SS#'s are not tied to vehicles. So every vehicle registered to John smith is tagged as owned by a cpl holder? Seems like something that would give the police quite a few false flags and become ignored...