Not Exactly, chromosome count is the major factor
That's a factor in reproductive isolation, but nobody uses it for species classification.
You may be interested to know that humans have a chromosome which is obviously a fusion of two chromosomes possessed by apes. How would you explain this if not by common descent? Apparently there
are natural processes that can change chromosome count in animals. (It's certainly well-established in plants, as you may know.)
You can read about it at:
Human / Ape chromosome differences