You are obviously much more aware of how this all works on a day to day basis that I am. And obviously with ADS-B (Automatic Dependent Surveillance Broadcast) the whole game changed. So yes, without a transponder airplanes are just a blip on an air controller's screen. And without the pilot or someone else communicating the position of the aircraft the controller has no way to identify the blip unless it was tracked from takeoff. However, military radar systems can track aircraft and missiles without transponders and determine their altitude.
I assume that this area is under surveillance by military radar systems where the turning off the transponder would not necessarily make much of a difference. But then it all comes down to who is watching, what they are looking for and what their motivations are.
I am not very familiar with the capabilities of different radars. I was only familiar with ATC radar. When I was in Vietnam, it looked someone threw rice on the scope. There were a ton of targets on the scope, but I only paid attention to the aircraft I was controlling. I didn’t care about all the other aircraft on the scope. We were totally dependent on IFF/SIF to identify the aircraft. Without it, we were up a creek.