Did Mary and Joseph enjoy a specifically conjugal intimacy?

". . . Mary has a higher allegiance. . . . And yet, in his trust in God, Joseph reveals he has a higher allegiance too.  Their shared higher allegiance, exchanged over the sharing of the most intimate secrets proper only to husband and wife

[(for example 1) the virginal conception and 2) that 'renunciation of' the sex that would have 'begun their own private family' and 'decrease[d] the scope of [a] married life' that had been 'completely turned outward toward all people equally', the sex that would have prevented their conjugal intimacy from being 'a loving preservation of [however still fallen sex] for the rest of us'; and perhaps even 3) an intimation, on Joseph's part, of the fact that the woman to whom he was married had been immaculately conceived)],

define them as husband and wife[,] and in their shared love and trust the 'secrets' hidden from all eternity remain hidden, precisely as marital intimacy. . . .
"Did Mary and Joseph have sex?
"Thankfully—not.
"Did they have the specifically sexual intimacy proper to man and wife, a 'sex life,' as we so unfelicitously call it sometimes?
"Assuredly—yes."

     John Cavadini, "The sex life of Joseph and Mary," Church life journal, 18 December 2007, italics mine.  Cf. Buccellati.  Their marriage was "for the life of the world".  And yet they kept some secrets proper to their married life and for that reason known only to the two of them, though proclaimed later by the Church (the Evangelists and the Church).