No they wouldn't.but the forces being applied to the box and the helicopter would be the same
The helicopter wouldn't be susceptible to friction - which is really where the debate lies.
I personally think the helicopter would move in relation to the truck (ie: if the truck were to move forward, the helicopter would appear to move backwards within the container). As others rightly say, if a box can slide about in the back of a truck during transitional movement, then a helicopter (which has no friction to help it along) would move about more.