It is possible but utterly pointless. The coveyor belt starts running and the aircraft starts engines. The aircraft has then first provide enough force to counter that of the belt passed through by the wheels/bearings.Assuming these have a low friction level,the counter-force is also low. ABOVE that it also has to provide enough force for normal takeoff. So you get normal force with an extra ie. 120% of the normal forces applied. Seems that lots of money is wasted on that extra 20% of power through fuel and bigger engines.

If the conveyor belt is in the same direction as the aircraft is taking off,it will be:
1) a huge challenge to get a belt big enough and able to support a full-size aircraft.
2) a waste of money, because one of those mile-long conveyor belts run over various suport wheels and stuff. These have friction,the belt on the driveshaft has some slip etcetera. I think the gains using this system(little to no fuel usage by aircraft on takeoff) would eventually not be enough. In my logical thoughts-stream it seems that the power used to overcome all these supports and wheels plus the slip is much more as an aircraft with about 8special bearings(assumed 8 wheels) with little friction.
3) it would be very dangerous,cos an pilot has to time the powering of the engines exactly,cos when he lifts off,he would have to use them again. Im sure you can train on that,but an normal take-off is easier for the pilot,thus making less mistakes.
4) The funding. a airport or government would have to pay for it,while they dont gain a thing for it, only the airlines. If they would have to pay for something that they don't really need and is expensive,they will complain and avoid these airports.

It will never happen. It can be realized,but would have no real point.