For sure, a society like this could not exist IRL for this very reason. People would refuse. They would sneak out and find each other, their feelings would overwhelm them as it has been in every other totalitarian society, past and present, where people have been kept apart. In the dark corners of the Earth where secret loves still exist, there are people hiding and sneaking and loving in secret... and they will continue to do so without the need for anyone else's approval.