They are linked by a commitment to each other. And their love is no longer a feeling that grabs you and can just as easily disappear. Love is not falling in love but loving. Loving is an active verb, an act of will, a decision, a resolve. Since there is no Protestant legal system, there can be no such thing as Protestant marriage.
Marriage is a social and civil act.
Not only in our day, but throughout human history, people have often lived together without any kind of traditional or official ceremony. For some Protestants the answer is yes. A life in common, a sexual life, both involve a reciprocal arrangement. A common roof and sharing a bed are hardly aspirins to reduce pain. Similarly with children.