IMO if your at the table getting ready to shoot and worried about your breathing you have the cart in front of the horse. I monitor my breathing techniques during the time I am waiting for my turn to shoot not while I am shooting. I use that time to do controlled breathing exercises to calm my heart rate, and provide more oxygen to my blood. This also clears up my vision and keeps me calmer in a stressful game. When I am at the table I concentrate on the layout not my breathing. JMO!!!!
That is a good point, and something that should be done with all aspects of pool. You should get to a point where you don't have to think about your stance, stroke, etc.
However, in the beginning, it might be a good idea to pay attention to it while you practice, to see if you are breathing properly, and if there might be some good changes to be made.