Yes, if you turn off the transponder in the cockpit the plane could go off the radar.
according to wikipedia there are 2 types of radar,
Primary- It is a passive radar that senses aircraft by pinging radio waves off the skin of the airplane.
Secondary Radar- which when it receives the primary ping, it responds with information about the plane.
If you shut off the transponder, i think you would deactivate the secondary radar, but the primary is passive that cannot be controlled from the plane. Im sure that they are researching if there were any radar hits that they could not id which plane it was.
The question is, is it possible that you can fly for awhile without any form of radar hit.... could they have gone "off the grid". I personally doubt it. But i have no clue of the range of radar etc.