I would say the added area is not wort the effort. I will question if the added area add drag or reduce drag. Same for sealing the box if you think about sealing the box so there will be no flow from one side to the other side of the wing. My guess is that these flows disturb the air and make as much or more drag than a larger area better sealed air brake. Note that the “projected” area into the air stream is the same even with a larger closed area.