You guys are a trip. Let me start by not even pretending to have read this entire thread, so if this is old news, forgive me.

The airplane wouldn't fly, and it doesn't matter that the engines move the plane as opposed to the wheels. In the original post, it said the belt has a control system that matches the PLANE'S speed - not the WHEELS' speed. Very important distinction because if that happens, the plane's wheels can spin at any speed but the plane's speed relative to the surrounding air remains zero.

If the plane doesn't move forward, there's no airflow (so-called relative wind) over the wings. No airflow, no lift; no lift, won't fly.

It wouldn't move forward because of the old "every action has an equal and opposite reaction" and the related laws of flight: lift must overcome gravity and thrust must overcome drag.

In our scenario, the "action" of the engines still produces the usual reaction (thrust) but not the usual result because a vital element is missing: the friction of the tires against the pavement. Take away this drag and the tires are still rolling on the conveyor belt but the result is different because the surface is not stationary.

The airplane will not move forward, so no lift will be generated and so gravity wins - the plane won't fly.

Now here's a new one for you:

Assume we're talking about a fixed-wing aircraft (i.e. not a helicopter) that is not a Harrier jet.

The plane's airspeed is 60 MPH but it is flying into a 60 MPH headwind. What is its speed over the ground?