As is usually the case, in aviation it's unwise to try to give a single answer to anything. If it were possible, the manual could replace airmanship or judgement.
I remember an RAF Bulldog student who bounced at Cosford and got into a PIO situation, with more than one bounce. The top of the nose-wheel oleo on these aircraft sits directly under the constant speed prop oil pump. The nose leg was deflected up into the pump, damaging it. This caused the prop to revert to the fully coarse position. The student decided to go around, but the engine couldn't provide enough thrust to allow a climb. The aircraft eventually overflew the entire length of the runway and crashed into a field outside the airfield.
Although it could be argued that not many low time students fly CS prop aircraft, even a basic aircraft could suffer prop damage, which could have a similar result.