Wrong!
If "one flesh" constitutes marriage, then Jesus would not have told the Samaritan woman the man she is now with is not her husband. By this, Jesus says marriage is something external to the physical union. Marriage is a committment to sustain the union for life. Fornication is the union without the committment.
(2) I Cor. 6:16, “What? know ye not that he which is joined to an harlot is one body? for two saith he, shall be one flesh,” which passage cannot be understood to teach that fornication establishes a true and valid marriage relationship.
Protestant Reformed Church. Acts of Synod and Yearbook 1987 PRC.
“He said to her, “Go call your husband and come back here.”The woman replied, “I have no husband.” Jesus said to her, “Right you are when you said, ‘I have no husband,’for you have had five husbands, and the man you are living with now is not your husband. This you said truthfully!”” John 4:16–18 (NET)