It would speed up the drawing up process. I would instead take frames out of the brood nest and place some to be drawn out into the brood boxes. Then take the box of foundation and place it on top of the two brood boxes. You really don't want to split up the brood too much. If you place and empty to be drawn out box of foundation between two brood boxes the upper bees might be isolated from the queen phermones and start to create queen cells. I do that to start up my queen rearing in the spring but I also separate them with queen excluders and provide an upper entrance till they have finished the cells. Then I move the cells to nucs. Hope this helps.
Dan