The question has already been answered correctly in this thread. In fact this question has been posted here before.
In short, yes it will take off. Planes move forward by engine thrust, not by driven wheels. So it makes no difference what is happening beneath the tires (conveyor, floating stationary on a river, etc.)
The question attempts to conflate an impact from the conveyor on the plane, but there is none. Even if the plane were moving backwards on a huge conveyor, the engines could still thrust the plane so that it first slows it's reverse speed, then eventually comes to a halt (relative to the ground and objects not on the conveyor), then the engines continue thrusting the plane to takeoff speed moving forward (again regardless of the rearward speed of the conveyor).
The comment about there being no wind is a red herring. It's not that there is no air, nor is it that the plane cannot create lift (by forward motion), just that there is NO wind (read the question again). Now if the question posed that there WAS wind, and that wind was a substantial tail wind, then that could impact the ability of the plane to take off. But with a long enough runway to accelerate, a plane could take off (theoretically, ignoring turbulence) even with a 1000 mph tailwind. A plane creates its own "wind" for lift by moving forward, and it can still do that on this huge conveyor.
Remember, the conveyor exerts very little rearward force on the plane (only friction on the wheel bearings). But planes land and take off at high speed, so their wheel bearing are designed to operate a high speed. Hence, it would take an incredibly fast conveyor to exert enough rearward force to stop the forward acceleration of the plane. But the question does not mention the speed of the conveyor (mostly because the conveyor is another red herring and is essentially meaningless).
Simple eh?