Qantas has also had a long association with a doctor in Remuera..
They cant report anything that hasnt been picked up in your medical examination - however I dont recommend you tell any fibs in your application for two reasons.
1) The medical is to assess your fitness and physical suitability to this role, and
2) If they did somehow find out they would have grounds for termination of employment and should they find out through an incident whilst on duty any health cover provided by the company would be void - which could be very expensive if you were away from home etc..
Sorry dont mean to be a big downer..