John 4:18 reports Jesus saying οὐκ ἔστιν σου ἀνήρ. Does the οὐκ govern σου or ἀνήρ? If the former, does it mean he’s a man but he’s not yours; and if the latter, does it imply he’s not a man, since one need not infer “spouse”? When can ἀνήρ mean husband as opposed to mere man? This verse is sometimes quoted to deprecate de-facto marriage (contra Gen 2: “For this reason...”?).
I'm not a greek guru and the following should be corroborated by one: οὐκ "governs" ἔστιν and σου "governs" ἀνήρ. So it reads "...isn't your man". One can look at ἀνήρ as "husband" and ἀνήρ as "man" as either two different words that are written the same ("homographs") or one word with two usages but either way, no, you can't tell the difference except in context. However, as I pointed out, the grammar doesn't support "the one you have now isn't a man". This is also made plain in that "the one" is not feminine the Greek.
The more interesting question you pose is whether or not the verse argues against de fact marriage. IE: does the process of God joining together two people together require a public ceremony or not. Great question. In fact, far beyond my pay grade.
In considering if two people are married or not one might want to consider what the government recognizes, Israelite practices, what one's "church" recognizes and what God recognizes, as well as the parties involved recognize. I can only say that there is no command or teaching that I'm aware of that makes the ceremony requisite for being joined before God. Paul seems to suggest that it is merely a question of "bumping uglies together" though he may have presumed that conception would occur as a result (1 Cor 6:16). However, the scriptures seem to presume certain marriage customs such as payment of a dowry:
Marriage affects more than just the two people involved and I'm going to refrain from what might be construed as advice. My own personal theological convictions are that marriage is a biological thing. Once two people conceive a child together they are divinely, irreversibly and literally made "one flesh" in the child. Marriage without a child is not a three-fold cord and is more easily broken:
Ecc_4:12 And if one prevail against him, two shall withstand him; and a threefold cord is not quickly broken.
People who conceive a child together are like scrambled eggs which only God can "put asunder":
Mat_19:6 Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder.
Nothing in this post is terribly authoritative I'm afraid because some things are beyond my reach:
Pro 30:18 There be three things which are too wonderful for me, yea, four which I know not: Pro 30:19 The way of an eagle in the air; the way of a serpent upon a rock; the way of a ship in the midst of the sea; and the way of a man with a maid.
KJV unless otherwise noted
The words for "man", in John 4:16-18, are all different parts of speech for anér (ἀνήρ). Whether it refers to "husband" depends on context. Basically, if it's combined with a possessive, it's referring to a man in the context of marriage (husband).
English treats the word "man" this way as well. Also, historically, husband had a more generic meaning until about the 13th century, when it began to refer specifically to a marriage context.
 He says to her, "Go, call the man-yours and come here."
 The woman answers and says to him, "I have no man."
Jesus says to her, "Well spoken – 'I have no man.'"
 "For you have had five men, and the one you have now is not your-man. This you spoke truthfully."
Jesus is catching the woman at a half truth. He refers to her husband (the man-yours), to which she says she has none. Jesus points out that not only has she had (sex with) five men, but the one she now has (sex with) isn't her husband (your-man). Whether that man is married to someone else is ambiguous. However, the word order changes between [4:16] (ἄνδρα σου) and [4:18] (σου ἀνήρ). So Jesus may be stressing that he isn't her man, but someone else's.
Regardless, he is showing his power by seeing through her (half) truth to the (entire) truth, which she immediately recognizes:
 The woman says to him, "I see that you are a prophet."