Absolutely. A HUGE connection.
I was asked to sing for my 5th grade class and then lost my good voice due to trauma in my early teens. In my mid thirties around 1975 I began a quest to regain my singing voice. I had no idea about breathing and emotions, energy, mental focus, sleep, anxiety, meditation, sex drive etc and why ancient teachings say "Breath is Life". I sure do now. The real issue is why, which, when, and how much is breath life.
I began relearning how to breathe via the emotional approach of Reichian therapy, took 156 weekly consecutive Reichian sessions and separate singing lessons and still could not sing. Yet I knew I had sand well before and in front of 300 people.
After some 20 years of working with various singing teachers (none stressed breathing very much or at all), hard and soft style martial arts, traditional and alternative health professionals I learned that they all had a lot to learn about healthy optimal breathing. In the nineties I at long last learned that breathing was the key to regaining my singing voice and that singing had a great deal to do with the management and containment of emotion.
Comments related to breathing rate of 15 being normal (too fast), mouth exhaling (helps develop snoring), heart rate variability (breathing rate is superior, easier and faster to monitor) and breath holding (locks up optimal breathing) are contrary to my understanding of what needs to be in place for simultaneous emotional balance, vitality and longevity.
But yes, any negative emotion one can breathe through properly and long enough will loose it grip on that person. Consider that an axiom.
The key is proper with a capital P and over a short enough time so as not give give opportunity for emotional re-stimulation and/or digression due to varying environmental sidetracking. Teaching optimal breathing development requires long term experience and eventually becomes part science and part art.
Begin here to learn about optimal breathing test.