Yes, it does. Several US Supreme Court decisions have upheld the authority of a police officer to search the area of a vehicle immediately accessible to the occupants for weapons when there is a reasonable belief established that there are weapons present that pose a danger to the officer. So...let's examine the typical traffic stop....
My wife is driving her car, which is registered in my name. She gets stopped for speeding. The license plate check before the officer approaches the vehicle comes back to me, a male who possesses a CPL. The officer may or may not get CPL information with the registered owner's name from the license plates. Specifically, in Florida, they do NOT. Officer approaches the driver's side and finds a female driving the vehicle - clearly not the registered owner.
Case 1 - wife informs the officer of her gun and CPL (in Washington where I am from it is a Concealed Pistol License). At this moment the officer has no verifying information that her CPL is real and valid or not. Just like he has no idea if her driver's license is valid or not which is exactly why they will verify it by calling in her information. The officer is perfectly within his legal authority to seize the firearm until he can verify that she has a valid CPL (especially since in WA a CPL is required to carry a loaded firearm in a vehicle). He is also perfectly within his legal authority to search the area of the vehicle from which my wife could obtain another weapon. Why? Because by telling the officer that she possessed the firearm she established for the officer the reasonable suspicion that she is armed - and he has no real way of knowing whether she is dangerous or not because he cannot know the validity of her CPL.
Now...case #2:
2. Same stop for speeding. He approaches the window, and everything goes like millions of traffic stops do - she gives him driver's license, insurance and registration. Nothing is said by either party anything about a firearm or a CPL. Officer goes back to his car and calls in her information and, let's say for fun that he finds out she has a CPL and it is valid. What has just happened? The legal authority to search her and car for weapons has been removed by the information that he has just received that IF she is in possession of a firearm, which she was not legally obligated to tell him about, the state has verified that she possessed a valid license for it and that should remove any REASONABLE suspicion that her possession of that firearm poses a danger to the officer because that is the exact excuse the state has used to require the CPL.
Millions of traffic stops happen every year where no mention is made of a gun or a license to carry a gun. The vast majority of stories you hear on these forums over the years of people who have had their guns taken from them by police officers during traffic stops (not to mention being handcuffed and searches performed) has been from people who have first told the officer that they were in possession of a firearm. I just won't take that chance.