If the conveyor belt is like a manual treadmill then it is unlikely for the plane to take off as the plane speed will always be matched by the treadmill speed and the plane will not move through the air thus it will not take off.
Now, it is also unlikely that you can create a belt like that without the plane's wheels creating enough friction to overcome a manual conveyor belt. The weight of the plane would likely push down enough to overcome the belt.
If the belt is a normal treadmill type of automatic belt then what will happen is that the belt will be turned on at whatever speed and the wheels will be turning at whatever speed, but once the engines are turned on the shit will hit the fan and the plane will move forward and IF the engines produce enough thrust to move forward faster than the treadmill and the belt is long enough the plane will take off.
Now, a problem may occur with the air speed generated by the belt itself. If you move a conveyor belt at 50mph it is going to move a lot of air. How much air and at what speed is the problem. Taking out the air movement of the belt let's say you have a plane with a takeoff speed of 50mph and the belt is moving at 50mph, the plane would have to move at 100mph to takeoff under those circumstances. The problem comes with the air moved by the belt. The movement of air due to the belt let's say drops the actual take-off speed by 10mph. Then the plane only has to go 90mph to take off....but what happens when it leaves the air space of the treadmill, what happens when it leaves that assistance?
Using the above numbers a plane's engines are creating enough thrust to move at 90mph, but because of the conveyor belt moving at 50mph the actual speed through the air of the plane is 40mph, still enough to take off given the air being pushed by the conveyor belt. Once the wheels leave the belt the plane will be thrown forward at 90mph and likely crash.
I say given the above situation the plane will leave the ground, but not for long...:) In fact, if the plane's take-off speed is 50mph that means it simply needs to move through an airspeed of 50mph. If you can create a conveyor belt that can move air at that speed you should be able to takeoff regardless of what kind of conveyor belt it is.
Alan