That question assumes a lot, and has different answers depending on who’s talking.
First, we must assume that they actually existed as human beings, which many historians doubt. But once we assume that, then we can look at different understandings about their relationship.
Within traditional Christian doctrine, of course, there’s no way. Since the gospels do not speak of his wife, Jesus was not married.
Yet, in that time and place a man would be married between 14 and 16 years old and could have raised a family by 30, which is when tradition says Jesus began his traveling ministry.
Unless, of course, he was a Nasorean (Nazarite), and dedicated to God in the temple (which the gospels say Jesus was), in which case, he would not cut his hair, not touch a woman (or anything “unclean”), and would avoid strong drink as part of the sacred vow his parents made for him when he was born…. (Remember Samson?) He could break that vow at any time, with the appropriate ritual, and what we call the Last Supper has elements of that ritual in it.
Another approach is to realize that the Gnostic literature (which the Roman Christians did everything they could to destroy) says that, at the least, she was his koinonia which can be interpreted as his “consort.” And it’s clear in those works that she understood his doctrine in a way that none of the men did.
In France and certain parts of Great Britain, it’s widely accepted that of course they were and that the St. Claire (Sinclair) family is their descendents through the Merovingian line of royalty (which the first Crusades placed on the throne in Jerusalem to fulfill the prophecy in the Book of Revelation).
Looking at the biblical account through the lens of a cultural historian, it seems necessary that the current “Son of God” would have participated in the heiros gamos, or sacred marriage, with the High Priestess of the “tall tower” (which is one interpretation of the word Magdalene), and that the feast at Bethany where the woman washed his feet with her hair was in fact a wedding feast (that being a not unusual wedding ritual at that time and place).
It can’t be an accident that all through Provence, La Madeleine is revered as not only a saint, but as the one who brought Christianity to the region, who maintained an ongoing relationship with her “bien-aimé” (her best-beloved, the resurrected Jesus), and who arrived on a boat from Egypt with a girl-child whose name, Sarah, means “Princess” in Hebrew. Especially not when one realizes that there was a large Jewish colony in the area and Herod himself had a palace there, to which he retired when he was dethroned.
So, given the history, it is possible and even likely that they had at least a wedding night.
My detailed thoughts on the subject are in my book, Mary the Magdalene: the divine feminine in Western Culture.