It would move on take off as it would be in an accelerating reference frame (not an inertial reference frame - one moving at a constant velocity).
Put another way, while the air may remain stationary relative to the plane*, the helicopter has mass and will want to remain stationary unless a force acts on it to accelerate it. In this case, the force will come from the air starting to move relative to the helicopter. This will cause the rotor to "flap-back", tilting the lift vector and providing the acceleration need to keep the model helicopter accelerating with the plane. In the course of achieving this, the model will have moved slightly towards the rear of the plane.
As Svenestron has quite correctly pointed out, if the plane has a constant acceleration, then that should be indistinguishable from a tilted, slightly stronger gravity force. As such, we'd expect that after the initial shift towards the rear of the plane, the helicopter would adopt a stable hover with the disk tilted slightly forward to provide the required acceleration.
Remember here as well that we are talking about those teeny, weeny little model helicopters that use flap-back to provide their stability.
Daniel
* The air actually isn't completely stationary relative to the plane. As the plane accelerates there will be a slight shift of the airmass in the plane towards the rear. This will cause a slight (very slight) pressure gradient from a slightly lower pressure at the front of the plane to a slightly higher pressure at the rear of the plane. It is this pressure differential that allows the air in the plane to accelerate at the same rate as the plane itself (much in the same way the pressure gradient between the earth's surface and space stops the air from accelerating downwards due to gravity). Of course, even this picture is simplified, ignoring transient "sloshing" effects as the air moves about.