Sure it would work.
The first colonists to other star systems aren't going to be ambassadors. They're going to be people in search of a better home. People in search of a place where they can live as they see fit. That's what space is all about. Trying new ideas and creating new cultures and civilizations. An endless frontier populated by a multitude of societies. The very fact that FTL is impossible will ensure that the vast bulk of Humanity remains in place. Cultural and societal isolation will be the rule.
Chances are that the first interstellar ships will be launched by private interests or by people living away from the Earth in deep space colonies.