A plane's lift is based on air speed, the speed of the wind over the wings. This reminds me of the myth they did with the car driving up the back of a semi, they were convinced it would suddenly accelerate and slam into the front of the truck, which of course didn't happen. But unlike a car, a plane isn't "driven" by it's wheels.
The big problem here is whether the speed the plane is traveling is air speed or ground speed. If the ground speed of the plane and the conveyor belt speed are the same, the plane won't be able to take off. Think walking the wrong way on a moving sidewalk at the airport or an escalator at the exact same speed, you go nowhere.
However, if the speed they are basing it on is air speed, meaning the speed of the wind over the wings is greater than the stall speed for the plane, then the wings should be able to generate the lift to take off, but there are some other complications as to whether it would actually leave the ground. In that case, it's tough to tell and I could see why the scale models would have problems. My guess if that's the case is no though.