Yes, the blocked tear ducts will cause the stuffy nose because of the interlinked eyes and ears nerves. You could find that your blocked tear ducts may get worse and cause other bad eyes problems if you don't treat it well. You should use the eyes drops to release the symptom. You could also use the warm compress to make the eyes feel better.
The stuffy nose is not a symptom of blocked tear ducts. Poor development of tear ducts or some illness of eye organization will lead to the blocked tear ducts. The eyeballs secrete tears every now and then; normal people will drain the tears into the nasal cavity. And people can hardly notice this process. If the tear ducts are blocked, the symptom is to keep running tear not the stuffy nose.