The clogged artery could cause shortness of breath if the clogged artery is clogged 70% or more.
Usually though if your artery is clogged and you're experiencing shortness of breath you'll most likely experience chest pain as well.
If you are constantly experiencing shortness of breath then something is not right either way and you should see a doctor about it since even though your arteries may not be fully clogged as of now it's possible that they could be on their way to getting fully clogged overtime.