That seems like a bad idea for a number of reasons
Although, I guess the benefit of being a P or VP (that other rich people wouldn't have) is that even if people know where you are, you've got top notch security and an air force at your disposal waiting to shoot down anything that may be coming your way.
It's publicly available information - any aircraft running a transponder (which is basically all of them, minus some select military aircraft) can be tracked via freely-streamed air traffic data. All you need is the callsign.