It's not so much the act of breathing - it's an emphasis,
using your breath to move your chest to, yes, signal to the partner
that Something Is Happening.
It's a signal alright - yep, you're alive and well.
More seriously:
I was taught and still practise that a slight lift of the torso and/or the right
arm indicates a collect - in other words a pause. Maintain that lift and
weight changes shouldn't be mistaken for sidesteps. It's subtle, invisible
to watchers but necessary if you subscribe to the view that everything
is lead. How you do the lift of course is personal and could indeed include
an inhalation to help lift simultaneously but it isn't necessary and you are
asking a lot of yourself. Best not to contrive it and just be natural.
Then a cross becomes an anti-clockwise rotation with more lift to indicate
that the free leg is intended to cross over. I've been stopped by one partner
from doing it so with some followers it works and some it doesn't.
It depends on what she has been taught I suppose.
Going back to another recent thread having lifted you now can indicate timing,
or even delay, the weight change and it really works with a responsive partner.
Please note that I've avoided the use of the word "rise". Rise to me in dancing
is rising from a flat grounded foot onto the balls of your feet which is
a very different thing. As BTM commented there is no up and down motion.