It comes up sometimes, usually if you’re in the jurisdiction that issued the permit.
The jurisdiction that issued the permit keeps track of the permits they have issued, and most counties keep a “local” file dispatchers run in addition to ccic/ncic.
I’ve had a few over the years, but many more people who told me during the stop.. without dispatch saying anything. Frankly, it’s pointless either way.
There is no statewide database.