It can go both ways. Of course plenty fresh air is good for you. However, deprivation of O2 does stimulate the body to make more oxygen carrying blood cells. That's the idea behind aerobic exercise and exercise in general. Work your muscles until they become oxygen starved so the body will produce more O2 carrying cells (RBC's).
But I can't see purposely depriving yourself of O2 via diminished breathing to accomplish the same thing as exercising does. Nor do I see how diminshed breathing could increase lung capacity.
I've never heard of buteyko so I'm unable to comment on it. But it sounds suspicious to me.