Breathing and timekeeping... I want to say tempo and breath rate really aren't supposed to be connected. Is a drummer supposed to breathe in tempo to the song? What about odd timings? No thanks.
Hey, whatever works for the individual. I already have enough to think about without trying to match my breathing to the tempo. What's the point? Sounds like an over-complication to me. Tempo lives in the mind, heart and soul, not the lungs. Using my conscious mind to tamper with an unconscious process seems like a waste of resources. Just one guys opinion.
A relaxed state works best to me, which is taking in the air I need without thinking about it. Holding ones' breath runs counter to relaxation. So does humming along, IMO a big energy sink.