What will happen on Airbus A320-200 series when during push back NW STRG DISC in not in the towing position?
The name says it all. NW STRG DISC or in full form the Nose wheel steering disconnect. And that is what exactly it does. It physically disconnects the nose wheel steering of the aircraft. In most aircraft, with nose wheel steering disabled, the wheel is allowed to caster. This allows pilots to maneuver the aircraft with the differential braking in case the nose wheel steering fails during taxi. So, yes even an aircraft the size of an A320 can be steered like a small aircraft with a castering nose wheel. So, a tow truck can turn the nose wheel of an A320 just like that.
The problem is that during push back the aircraft engines are started. With the engines started the aircraft hydraulics are powered and pressure is sent for nose wheel steering. The nose wheel, without any inputs always centers it self. During the push back if the nose centers it self, it can damage both the tow truck and the nose wheel of the aircraft. To prevent this the nose wheel steering has to be disconnected for push back. In the A320, there is a lever on the nose wheel which can be put in the towing position. Once it is placed in position, a bypass pin is inserted to ensure that the lever is held in place. Once the lever is positioned an ECAM memo NW STRG DISC is displayed in the cockpit in green. The message turns to amber colour when one of the aircraft engines are started. The whole point of the ECAM message is to increase pilot awareness so that you do not mistakenly leave the lever in tow position before commencing the taxi.

An Airbus A320 with nose wheel bypass pin inserted.