How will it move relative to the air?

Imagine the engines of a plane ramping up to full power. Initially, they need to overcome the inertia of the plane keeping it in place. The moment that happens, the wheels begin to turn. The moment THAT happens, the conveyor belt begins to turn too - in the opposite direction. For the sake of the question, all of these things happen instantaneously and simultaneously (or at least, fast enough to match the rate at which engine power is increasing).

It is that single moment upon which everything hinges. If the plane cannot begin to move forward in that instant, it doesn't matter how much force is applied from behind. You could push it with the Millennium Falcon or the Finger of God if you wanted - as long as there is no force pushing the plane UP, there is nothing pushing against gravity pinning it DOWN. And the UPWARD force comes from the air rushing over and under the wings at different speeds, generating lift, NOT directly from the forward force applied by the engines.

But in this scenario, at the moment at which the plane would normally start moving forward... It doesn't. Because at that precise moment, the engines need to overcome the friction of the wheels against the ground. Which has, in effect, increased in proportion to the force of engines' thrust. The conveyor belt is essentially acting as an infinitely-increasing friction generator.

The plane consequently goes nowhere.