Yep, some will do that. Mine is located above the rear view mirror so you can't see it just standing beside the car.
I'm sure that license plate reflector will have the same effect with police and you can't hide that, so thats something to consider.
My radar detector has paid for itself many times over as the police using laser are still only a small percentage so it has saved me from all the KA band radar as that is the perferred method due to cost...
And generally cops wants to just park and leave the gun on all the time and just look at the dash for your speed, takes alittle more effort to hold up the lidar gun and pull the trigger on everycar, so I count on a little lazyiness there.
Also, the lidar can't go thru the cop car windshield so they have to get out of the car or park long ways so they are obvious to spot if you keep your eyes open and pay attention..or they are standing on top of bridges, another dead giveaway from quit a distance.
That being said, I've been stopped a number of times without receiving a ticket with the radar detector up before I moved it up to the mirror.