Can a military pilot make his airplane invisible for the ATCs?
Radar systems have 2 aspects, the primary and secondary systems, or the Radar and the interrogator. The radar sends out a RF signal and receives everything that is returned on that same frequency, and performs calculations to determine the azimuth and range of everything it receives. The interrogator sends out radio pulses which transponders in aircraft receive and decode. The transponders then transmit data on a different frequency than what was received. The interrogator then receives that signal and decodes it and correlates it with the primary radar data to tell the operator that 'yes, that is definitely a valid target' and gives the info on the flight to the operator.

You can turn off the transponder, but all that will do is make it so that the ATC won't be able to see a correlated flight, (one that is definitely an aircraft and not just noise coming through the primary radar). The screen would still show a blip where the radar picks up a signature though. If the plane has radar absorbent material or is close enough to the ground, that would get filtered out as noise.

An ATC, who is used to only working with aircraft who want to be seen, and thus keep their transponders on, might be fooled by this. But a military radar operator might not be so easily fooled by this.