Most likely my gun would be locked in my glove box, since I pretty much keep it locked there when I'm driving. I, therefore, would expect it to be there locked up, unless the police had some reason to get a court order to break into my glove box.
BTW, I drive a stick shift, so it's no big deal for me to quickly take my keys out of the ignition and unlock the box, while the car is still going (coasting). Safe? No. Doable? Yes.