Lets put it this way. Having an aircraft with its parking brake on and on a conveyer should essentially do the same thing. The aircraft will be stationary in point of place. Now, if you add full takeoff power, with the parking brake on, the airplane might, if the brakes are poor, being moving forward quite slowly, due to the airflow over the propeller. Overall, it will remain stationary. If an aircraft is stationary, even WITH full power, is there enough airflow over the wings for it to takeoff?
No. But that's not the point.
The propeller is designed to pull it's way through the air. And that's what it does. Conveyor or no.
End of story