The original question says "STANDING" which implies no movement. In that case, no movement = no flight.
But assuming no trickery in the question, can a plane take off from a conveyer belt if the belt matches the planes speed, but in an opposite direction.
ABSOLUTELY!
NO. 1
If a car was on a conveyer belt and was running 100mph according to the car's speedometer and the belt was moving 100 mph in the opposite direction, then the car would not move. It gets in propulsion from the ground, or conveyer belt in this case.
NO 2
Now although it may not be possible, imagine a plane pulling that same car and relative to the ground, they are both now moving 100 mph and the con. belt is still moving 100 mph in the opposite direction.
So why is the car not moving in no. 1, but it is in no. 2? In no. 2, the plane which is pulling the car is using AIR to pull it forward. Yet in no. 1 it is using it's wheels to provide acceleration. Therefore, in no. 1, of course it would not move relative to the ground.
SO FOR THOSE WHO THINK THE PLANE WILL NOT MOVE, DO YOU THINK IT GETS IT FORWARD MOVEMENT FROM IT'S WHEELS.

IN THAT CASE, AS SOON AS THE PLANE LEFT THE GROUND, FRICTION WOULD SLOW IT BACK DOWN AND IT WOULD RETURN TO THE GROUND. THAT'S LIKE PUTTING WINGS ON A CAR. WHEN IT GETS UP TO SPEED, IT WILL LEAVE THE GROUND, BUT IMMEDIATELY RETURN BACK TO THE GROUND.
Now back to the original question, the plane gets it's propulsion by pulling itself through the air. Air provides the stationary resistance for the plane to accelerate against, The conveyer belt would have no relevance to the planes acceleration since it uses air.
If you held a radio controlled plane in the air and it was revved to full throttle, would you feel it pull? For those that think the wheels affect it, I guess you think it would not pull against you since it's wheels aren't touching the ground.
Imagine the cub scout wooden rally cars? Strap a large bottle rocket to it and place it on the con. belt. Will it move with propulsion coming from the bottle rocket? YES Now detack the rocket and attach motors from a radio controlled car to the wheels. Accelerate the car with the remote control motors attached to the wheels. Will it move now? NO
If a fish were swimming 3 mph directly against the flow of water which is flowing 3 mph in the opposite direction, you could watch the fish swim "in place". (Kinda like those swim at home pools, where the water is flowed through a short pool and you swim against the water) Now a fisherman catches that fish from an upstream direction. As he reels in at 3 mph, the fish moves closer to him at 3 mph. It moves now because it is getting it's moving force from something other than the flowing water.
So as long as the plane gets it's acceleration from something other than the "flowing water", it is going to accelerate and fly.