>>1
Yes, assuming the treadmill is turned off.
If it is on, then it depends on the speed of the tread and the direction of the plane since if it were travelling fast enough the resistance on the axil of the wheels of the plane will heat up and melt, increasing resistance between the plane and the tread till the plane doesn't have enough power. However if the plane were facing the other way it would be catapulted into the air.
If the tread mill is too slow to make a difference the wheels will be able to reduce resistance enough for the plane to gain enough airspeed to take off.