I would suggest that BOTH camps are correct at some point in this scenario. :idea
There is a certain amount of rolling resistance in the airplane's undercarriage. (In any vehicle. You can measure it by determining what slope it takes for the vehile to start to roll on its own. Once it is rolling, this force is somewhat less but that's not really important here). Therefore, as the plane powers up, until the thrust overcomes this rolling resistance, the plane will be influenced greatly by the action of the conveyor. It will move with the conveyor (backwards).
Now, apply sufficient power to just balance the rolling resistance against the moving conveyor and the plane stays stationary, there is no airflow over the wings and there is no flight., Chalk one up for the non-flight group!
However, once you apply more power than is required to overcome the rolling resistance and the plane will start to move forward. The conveyor will try to speed up to counteract this motion however it will not have a significant impact since the resistive force that "ties" it to the moving conveyor is already overcome by the power supplied by the engine.
This rolling resistance is not significantly impacted by the speed of the conveyor; once you get something rolling any increase in speed of the conveyor will only speed up the rotation of the wheels. There is some increase but not important compared to the power of the engine involved. (In cars, it takes more power to go faster not because of increased frictional resistance, but aerodynamic loads.)
Therefore, the plane will be able to add power until it moves forward on the belt, even as the belt itself speeds up, and generate airflow over the wing, lift and hence, flight.
Chalk one up for the flyers. :clap:
The key points to remember are that the plane does not require contact with the ground to apply power (so people on treadmills etc do not duplicate the scenario since you rely on your feet interacting with the belt to propel yourself forward) and that the rolling resistance is not ever increasing. If it were ever increasing, cars would not continue to speed up rolling down hills until the aerodynamic forces overwhelmed the situation.
That's my story and I'm sticking to it. :LOLOL