The DASS ("Defensive Aids Sub System") of the Eurofighter Typhoon can "delay/hamper/prevent aquisition by enemy RADAR", using powerful jamming transmitters in the wing tips. It also has towed jammer transmitters ("Towed Decoy", being towed behind the airplane by 100m of Kevlar line). Via Cross-Eye-Jamming, it can also make Monopulse-RADARs blieve that the plane is at a different position.
The Eurofighter Typhoon can dispende chaff, which can block simple RADARs, but is mostly useless against Doppler RADAR.
All these counter measurements are primarily targeted as a defense against RADAR-guided missiles. These counter-measurements show up on the RADAR displays. Chaff will produce a large RADAR echo (trying to convice the simple brain of an approaching missile that the chaff is a better target than the airplane). Jamming will show up as noise on the receiving RADAR. The noise will will occupy a sector of the RADAR image. Depending on the strength of the jammer and the quality of the RADAR, the sector may be wider or rather tight, but it will always point into the general direction of the jammer. The RADAR operator will know that there is a RADAR jammer in a certain direction, but he will not know altitude and distance. Obviously, networked RADARs, which combine data from RADARs at different locations can triangulate the position of the jammer.
But there's always the classical approach: low altitude flight, preferably in a hill/mountain region.
In any case, it will be the last flight the pilot ever did as a licensed pilot.
Edit: Oh, yes, Anti Radiation Missiles. Most probably the AGM-88 HARM ("Highspeed Anti Radiation Missile") in case of the Eurofighter Typhoon. These will definitely make ALL aircraft invisible to a RADAR. Useful in a range between 25km (if launched at low altitude) and 80km (if launched in the stratopause, a height of 50km or so), it will approach a RADAR at a speed of Mach 2.9 or above. Of course, the RADAR operator will, most likely, notice that his RADAR just got destroyed by a missile. The NATO Counter-Surprise alert state will about immediate jump to SCARLET. Military RADAR (like the AWACS ("Airborne Warning and Control System")) will, most likely, have already detected the missile attack. Anti aircraft weapons will be manned, fighter and bomber aircraft will be readied and awaiting combat orders. The USA will, most probably, also go to DEFCON 2, with a stand-by for a possible increase to DEFCON 1.
What exactly is the "unintened purpose" of the Austrian pilot. Trying to impress his girlfriend, maybe? Hm.
More plausible is what Peter mentioned: impersonating another flight by switching transponder codes. The ATC will, most probably, notice when a flight does not behave as expected, is in two places at the same time, or is present at the wrong time.
Also note that there a different ATCs: Eurocontrol for the Upper Air Space. Austro Control for general Austria, Deutsche Flugsicherung for general Germany, plus the individual ATCs for the airspace near the individual airports.