the box *should* be fine, even if ran with no oil provided you do as suggested and throw a load in it flush, then refill.
As the dark lord says, most of the box does turn in neutral, but gears actually get ran dry during the manufacture stage, for mesh and tolerance checking. good chance you will be fine with residual oil coating.
For reference, i drove a getrag 300 miles with NO oil in it, and it lived with a top up. ;)