Will a cat breathe through its mouth if its nose is stuffed up?

I was just wondering if every cat will breathe through its mouth if its nose is blocked or if it will just struggle and not get enough oxygen to its brain trying to breathe through its nose in vain. I am concerned my cat may have done this as he has symptoms of brain damage.

Yes the cat will breath through its mouth, and yes, it's a serious indication that the cat needs to be seen by a vet asap.

The other perhaps greater concern is:  a cat eats by smell.  If the cat can't smell, he may not eat, which may lead to fatty liver disease.  There is one such cat in the cattery I volunteer for.  The family he was with did not seek medical attention when he first developed a cold, so he quit eating; by the time the family took him to the vet, he was in liver failure.  His prognosis remains guarded--ten days after being returned to the cattery and receiving medical care and assist feeding.