What on earth has cog got to do with it? If CoG affects the reading on the scales, does that mean that the scales would read different if the pilot were sat down or stood up?
In a steady hover, the air is accelerated by the blades and the mass of this accelerated air causes a reaction force equal to the mass of the helicopter. The bottom of the box decelerates this air, causing a reaction which is measured on the scales. I agree that the reading on the scales will change if the aircraft climbs or descends within the box, since the aircraft will be accelerating, but once in a steady climb, the scales will return to a steady reading. In other words, the scales would read the mass of the helicopter plus box, unless the aircraft was starting/ stopping a climb or decent. What is more, the hover height will not affect the scales (ie independant of ground affect).
I wish Santa would bring me a Jet Banger in a box, or even better a twin squirrel....... he can keep the scales!