Yes, all receivers also emit a signal. That's how RADAR detection works. This is used by the police in some countries to detect cars which are using RADAR detectors. It's known as a radar detector detector.
Ordinary GPS in not permitted as a navaid if it's not got some sort of certification (forgotten the details, sorry) Basically, they have to ensure the accuracy of the GPS position.
Mobile phones / WiFi is a very bad idea around any critical wiring. We've all heard the buzzing sound through headsets / speakers when someone's phone goes off. Now imagine this signal going into instruments / computers. It can easily corrupt data, which is why in data centres (big buildings full of computer servers) mobile phones are definitely banned.