I have one of those "cases"; its a Sneaky Pete holster. To any of us on this forum it is a dead give-away that I am armed, or foolishly carrying a large calculator or small tablet in a gun case. But to the average Joe-public, it tells them nothing at all. I had mine before we had concealed carry here in Illinois, thinking I might use it when traveling to Wisconsin where my Utah permit is recognized. But just to see how much it really shouts "gun" to even those in the know, I wore it on a visit to the State Capitol, keeping my larger smart phone in it. Remember that this was about 3 years ago, when any concealed carry was illegal here in Illinois. I had contact with several of the police at the Capitol building, and no one said a single word about my holster. Nor did any of the public.
That said, I have not actually used it as a holster since that time at the Capitol, but I am never surprised at the total lack of observational awareness exhibited by the public. Personally when I carry concealed I want to give no indication of such to anyone. I wear no firearm related clothing, have no firearm or NRA stickers on my car (I am a Life member) and I am sure that to the general public I am just another somewhat overweight old guy with a beard, i.e., an invisible person. But to each their own.