Exactly speaking, it won't. Pink eye are often due to eye infection, that is, bacteria and virtues cause some eye disorders include pink eye. Pink eye, also called conjunctivitis, is common and not serious. Blocked tear duct is pathway partial or complete blockage, which will automatic clean in 6 months for babies. While, adults need to receive medicine treatment. Generally speaking, blocked tear duct is hard to cause pink eye. But we cannot rule out special circumstances, such as your eyelids are broken or infection during your healing of blocked tear duct. All in all, take good care of yourself.