Reasons can be given all day as to why it will take off. But all the babble is bending the rules in the given situation. The question is simple as it it stated. The the plane occupies the same geo position on the face of the planet - it's not going to get lift under the wings. Thus, it's not going to fly.
In simple easy to understand english:
If the aircraft overcomes the speed of the conveyor it will move forward through the air which causes a vacuum over the top of the wing, thus creating lift and it will fly. If does not, it will fall off the a$$ end of the conveyor.
Assuming power is gradually applied to the conveyor causing it to move faster under the aircraft, and the aircraft is powered up in order to keep the same position on the conveyor relative to the ground - which is the assumption made by the question - you've taken out the most basic ingredient in flight - lift.
No lift, no flight.
Try it this way. Grab a piece of plywood, jump on a tread mill, turn up the treadmill to the fastest setting. Feel anything tugging at the sheet of plywood? No? Gee, think maybe because you're not getting any lift?
Keni

The only thing you never want to hear a Navy ordnanceman say.