If they treat you any differently in any of those cases because you don't have a CCW they are stupid and letting their families down.
The police deserve to have all the information they can get when dealing with a potential bad guy.
They certainly do and get it when they run your plates, including your arrest record, if any. I'm just saying that not knowing you have a CCW doesn't affect their safety one bit, so they have no need to know.
The one caveat I would add here (though it's not sufficient to justify the intrusion of privacy) is that if a vehicle's driver behaves in a manner inconsistent with being a super-law-abiding citizen but the vehicle's owner holds a CCW, that would increase the likelihood that the vehicle is being driven by someone other than the owner.