I'm not sure what the Orthodox church can do about people outside of it; common-law marriage, civil marriage, non-Christian religious ceremonies--I always considered such marriages to be valid. Why wouldn't they be?
But of course, converts to Orthodoxy need to do what the church requires of them.
Baptism is the gateway to the other sacraments, so if someone is not baptized, they are not married. If you use natural law, you could argue that these relationships are natural unions and are not fornication--that is the perspective I agree with--but they are not sacramental marriages.
The Russians tend to not marry converts because joint reception of Holy Communion was the ancient practice to seal a union and that "suffices" to complete the union of those converting. The Greeks have adopted a formal practice of marrying converts to one another in the Church to emphasize the sacramental blessing that occurs in the Church and since Greeks tended in the later centuries to baptize more frequently this was simply the established custom.
When I converted to Orthodoxy from Catholicism, my wife and I were baptized, chrismated, received communion, and then married to one another all at the same time. It was a very moving experience, one I will cherish forever.