Mmmm;
The box is airtight.
The box is cardboard.
From the start point of the experiment, a vacuum will be created due to the engine and pilot consuming the fixed volume of air.
This vacuum will increase in strength ultimately causing the box to collapse in on itself, resulting in the weight of the wreckage + box + pilot being the same as at the start of the experiment.
However, assuming the integrity of said box has not been compromised, ie is still airtight, the resultant carbon dioxide that was produced, being heavier than the air it has replaced, would cause the resultant wreckage on the scales to weigh more than at the start.
Just a thought.