It will take off.
The thing to remember is that the wheels aren't directly connected to the propulsion system. They're essentially frictionless meaning what happens
to them has no effect on what happens to the rest of the plane.
Think of it this way. Say the plane is moving forwards at 100kph. That means the conveyer is moving 100kph in the opposite direction. The wheels would
move at what would feel like to them to be 200kph. Because the wheels are frictionless there is no effect on the plane itself. To the wheels there is
no difference between this situation and the plane travelling at 200kph on a fixed ground. The wheels in this situation only support the weight of the
plane, they have no effect on the forces in the x direction. It's as if they weren't even there. In fact it doesn't matter what speed the conveyer
is travelling at.
From my picture above the plane is providing force in one direction from the engines. The conveyor is providing force in the other direction and
because the wheels are frictionless there's no connection between the two.
In reality there is some friction in the wheels so if the conveyer is travelling at 100kph the plane is travelling forwards at 90kph. It would make
the beginning (low speed) difficult but at takeoff speed the effect would be negligible.
It does get confusing and is very counter intuitive but once you realise that a planes wheels don't provide the propulsive force like a car it starts
to make sense.
P.S. ph34r my l33t dr4w1ng sk1llz