I am a biologist - no.

“Breathing” is a quick vital sign that can can be used on someone who is incapacitated. It can help guide what medical intervention is needed.

But physically breathing using your diaphragm muscles is not a requirement for something to be alive… your body is still using oxygen while you hold your breath, after all. Lots of animals don’t need to physically breathe at all, and there are tons of organisms other than animals that don’t even need oxygen to live.