The conveyor belt can be moving at 1000 kts and the aircrafts wheels can be turning at 1000 kts but, if there isn't sufficient airflow over and under the wings, the aircraft will not fly. (unless its a Harrier, JSF etc)
The aircrafts wheels are free-spinning!! As long as the engines provide enough power to overcome friction within the wheels, the aircraft WILL move forwards relative to the air! There will be relative airflow, and the aircraft will fly!
What you say above is technically correct, because for the wheels to be spinning at the exact same speed as the conveyor belt, the aircraft must be stationary relative to the ground/air. You must realise that once the aircraft moves forwards relative to the ground/air, the wheels will spin FASTER than 1000kts, if the belt is going at 1000kts.
Try taking a small model a/c to LGW or similar and try it on a travelator! If the aeroplane has sufficient airflow over the relevant surfaces, in excess of its stall speed, it will fly, if it dosen't, it wont get off the ground (travelator).
I'll bet money on it flying. The motive force will be applied to the AIR, not to the travelator surface! There are only a few possibilities here :-
1. The engine is left off/idling and the travelator builds up speed slowly enough that the friction within the wheels is not overcome. The model a/c moves backwards with the travelator.
2. The engine is powered up JUST ENOUGH that the frictional force within the wheels is overcome and the aircraft remains stationary relative to the air/any fixed point. This is exactly what would happen when the aircraft taxis on normal ground, except in this case, the wheels don't spin because of the aircraft going forwards - they spin because of the travelator belt going backwards underneath.
3. The engine is throttled up to full power, or any power setting beyond that used in outcome 2, above. The force applied between the propellor and the AIR is great enough to overcome the frictional force within the wheels, AND propel the aircraft itself forwards through the air. The wheels spin at the speed of the conveyor belt, PLUS the speed of the aircraft moving forwards. The aircraft easily takes off.
The ONLY thing allowing the conveyor belt to move the aircraft backwards is the friction within the aircrafts wheels and axles. As soon as this friction is overcome, the aircraft is able to move forwards just like any other taxying aircraft on normal, stationary ground! The only difference would be the wheels spinning at a greater speed -which DOES NOT MATTER because the motive force is applied via the air. The wheels only spin at this speed because they are free-spinning, and able to - NOT because an engine is making them (Not directly anyways...the increased speed is of course a component of the engine moving the rest of the aircraft forward).
The aircraft will fly!