The plane will take off...Here is why
Lets start by looking at a car in the situation instead of a plane. In a car, the wheels are what drives the car foward. In this case, the car would remain in place relative to the conveyer belt due to the belt moving in the opposit direction.
Now, in the case of the plane, the wheels do no driving at all. The wheels are only there to reduce friction between the ground and the plane itself. The actual force that moves the plane is that of the jet engine sucking in air from the front and pushing it out the back.
Just a little more explaining to do, and then all will be understood.
If you sit a car on an icy lake that has 0 friction between the wheels and the ice, the car will not move. This is because the force that makes a car move the friction between the rubber tires and the ground. With the plane, the wheels do not drive anything, they simply help the plane roll along. So, a plane sitting on an icy lake can take off even if the wheels have no traction.
So to sum it all up...THE PLANE WOULD TAKE OFF IN THIS SITUATION.