Practically very unlikely, theoretically sure, when you're short of breath. The pectoralis muscles count as a accessory muscle of respiration.

Even trapezius and latissimus dorsi are accessory muscles of respiration, so on your back day you can have a harder time breathing when the diaphragm isn't enough.

"Accessory muscles refers to muscles that assist, but do not play a primary role, in breathing. Apart from the above neck muscles, the following muscles have also been observed contributing to respiration: serratus anterior, pectoralis major and pectoralis minor, trapezius, latissimus dorsi..."

https://en.wikipedia.org/wiki/Muscles_of_respiration#Accessory_muscles_of_respiration