One would have to read those who are experts on the Jesus Prayer…on this aspect of it…
I have often seen a caution in regards to this aspect…that one should have a spiritual director who is experienced if one wishes to add breathing to it…
Though perhaps they meant more prolonged periods…(??)
Also this is from the Congr. for the Doctrine of the Faith:
- Eastern Christian meditation32 has valued “psychophysical symbolism,” often absent in western forms of prayer. It can range from a specific bodily posture to the basic life functions, such as breathing or the beating of the heart. The exercise of the “Jesus Prayer,” for example, which adapts itself to the natural rhythm of breathing can, at least for a certain time, be of real help to many people.33 On the other hand, the eastern masters themselves have also noted that not everyone is equally suited to making use of this symbolism, since not everybody is able to pass from the material sign to the spiritual reality that is being sought.
Understood in an inadequate and incorrect way, the symbolism can even become an idol and thus an obstacle to the raising up of the spirit to God. To live out in one’s prayer the full awareness of one’s body as a symbol is even more difficult: it can degenerate into a cult of the body and can lead surreptitiously to considering all bodily sensations as spiritual experiences.
ewtn.com/library/curia/cdfmed.htm
Note too that the above is not saying the Jesus Prayer is not good…it is good! It is referred to in fact in the Catechism of the Catholic Church…and the Doc. above it notes that some have found it “at least for a certain time” to be helpful.
I do not want to say categorically “do not ever associate breathing with it” but to simply note the cautions I have read in the past (not at my fingertips right now to look into the question more)…