Yup. Look at all the older pro racers. That "flabby gut"? They learned years ago to relax those abdominal muscles so they could pull that diaphram down. Another trick - exhale. This from a swim coach. She stressed it matter little how much we inhaled and everything how much we exhaled. Reason? It is by exhaling very deeply that we clear the old air from the lowest portion of our lungs - where the lung's best oxygen receptors hand out. With a partial inhale, what we didn't expel is left nullifying those super oxygen receptors. Her words were that if we exhaled everything (easy in freestyle; you have a long stretch with your face underwater) and only get a 1/4 breath because a wave just slapped our face, we would be way ahead of the guy doing less than complete exhales.

And now, on the bike - when I am dying on a hill, remembering those words and exhaling everything, despite that seeming completely wrong, I always speed up near instantly. At the hill top, recovery happens much faster.

And to the OP's question - yes, with inadequate oxygen your legs will hurt more. Lack of oxygen, either through huge muscle demands or lack of supply, hurts, both upstairs (lungs, etc, and in your legs. You can ride a higher gear. This wil lower your oxygen demand as you will be in anaerobic mode, ie a metabolism that doesn't use blood oxygen. Helps with this issue, but has its own limitations.

Ben