Mike,
The concept of uniting for the purposes of physical pleasure, procreation and unity of male-female is not at all sinful.
Marriage by all points is that unity.
So, immediately when a man & woman enter into physical (in some beliefs, mental or emotional) connection, it is a marriage.
It is well known for many years, men had many wives -Solomon included. The sin enters when one of them departs for the lust of someone else or an unnatural source of affection/unity/pleasure.
So, sex is the marriage itself, yes.
Adultery, fornication (arousal of desire/passion without care or cause for unity, momentary satisfaction), divorce, etc would be the sin.
James