Aircraft do not require friction with the ground to accelerate in the same way that a car or bicycle does. It would accelerate at almost exactly the same rate as it normally and take off with ease.
This. If you, however, were to increase the velocity of the belt to the point where the friction would prevent a plane from moving, the most noticeable effect would be the wheels melting from the heat, and the aircraft then flipping over forward, due to the friction force being unaligned with the forward thrust of the engines. Likely followed by an explosion of slag resulting from the frictional heat instantly melting any part of the aircraft it came into contact with.
To take off, aircraft need air speed; ground speed is entirely irrelevant. It's why aircraft like taking off into a headwind, and hate doing so in a tailwind. A 15 MPH headwind means the aircraft has to have a 15 MPH lower ground speed to take off; the opposite goes for a tailwind. Same goes for landings; for a headwind, you land at a lower groundspeed, and so have to slow down less on the ground; tailwinds require more slowing down. Which is why aircraft carriers try to orient themselves into the wind; it minimizes necessary runway length and takeoff/landing force.
Funfact: in Microsoft Flight Sim X, you can modify wind speeds. If you set it to a headwind above the required airspeed velocity to takeoff in a particular aircraft, you can VTOL that aircraft; be it a tiny 1-seater or a 747. Though, naturally, flying in hurricane force winds has detrimental effects on your ability to fly.