Not much. I understood MassiveD's post because I deal with increasing lung capacity in my work.
With thumbs inward, ala flats, you are ever so slightly restricting expansion of the rib cage. Thumbs forward, ala drops, not so much, thumbs outward better (but impractical). Flats with bar ends accomplish what drops do. It has a little to do with flexion/extension of the pectorals but more to do with shoulder position. Shoulders rolled forward restricting ventilation, shoulders back and up, like a cruiser, opening the rib cage. One exercise we do is to start with hands inward (in the lap) and then extended outward with thumbs moving into a double hitchhiker position (like a picture of the anatomical man) breathing deeply as you go.

Hand position and a wider stance with the hands may allow the rib cage to open more but that has to be balanced with compression of the diaphragm (79pmooney makes a good point about stretching out) and how practical those results are for a normal healthy cyclist. Most of us can ventilate well enough for touring (working at less than capacity) at any angle though I bet there is some research for high end road racing.