Can Cats Cheyne Stoke When They Die?

Do you mean Cheyne -Stokes breathing? This is intermittent breathing, with periods of no breaths followed by periods of hyperventilation, associated with heart problems, also common in the elderly.
There is no way to know how much longer he would have lived. What you need to ask yourself is, would that time have been enjoyable for him? When the answer is "no", then keeping the animal alive is something that the human is doing for themself, not the animal.
I think you can rest easy, you did the kindest thing.

My 3 1/2 year old Ragdoll cat experienced Cheyne-Stokes breathing as he lay dying in my arms this Sunday at 2:20am after a lengthy illness.

It was a terrifying, horrible, and obviously painful experience for my kitty, Elvis. It was quite shocking for me and my husband, as well.

When taken off of life-support, after a lengthy illness of his own, my uncle experienced Cheyne-Stokes breathing. 

I have seen it in a human one time. I have seen it in an animal one time. It is very real in both. It is also something I wish to never be a witness to EVER again!

Cats don't chain stoke when they die, actually they do this because of their old age and in fact they need to do it, without doing it they will not be healthy. That's why your cat do this. In fact the normal age of cat is 14 years i.e. It is an average age of cat and your cat is too old now so he do this.