Boy, I wish there were ‘easy’ (i.e., ‘short’) answers to your questions.
But, you’re asking questions that require precise answers, so…
So do two become one flesh ONLY in the case of a valid marriage?
First off, it’s important to note that the Church has the responsibility and authority to protect and administer the sacraments. This means that, if the Church has spoken on the validity and liceity (i.e., “what makes this a sacrament” and “what steps should be taken in the celebration of the sacrament”), then the Church is fulfilling its duties to properly define and protect the sacrament.
So, given that the Church
has made these kinds of statements in the context of marriage, then yes: what God intends (the “one flesh union”) only happens in the context of a
valid marriage.
Furthermore if it is at the exchange of consent, can two become married simply by consenting one to another with no formal process?
I would answer you ‘no’. Here’s the thing: way back when (think, like, early medieval times), there was no formal process. People would go off, proclaim vows to each other privately (with no one else around), and be married validly. (After all, at that time, there was no formal process like we have today.) The problem was, people were being victimized. A couple would marry, and then one of the spouses would find someone who was a better ‘catch’, and then say, “what? I married
her? Oh, no, you’re mistaken. I never married her. I’m free to marry this rich girl over there!” And, in that instant, the other spouse had no recourse – they were validly married, but could not prove it, and therefore, were out of luck.
So, the Church stepped in, for the sake of the victimized spouses, and established rules. Marriages would have to take place publicly, in a church; they would have to be witnessed by an official representative of the Church (a priest or a deacon); the marriage would be officially recorded by the Church in a parish register. This is where the notion of ‘form’ comes in. These requirements do not proceed from Christ’s discussion of marriage as found in the Scripture, per se; they proceed from the Church’s valid exercise of its duty to regulate the sacraments.
The Catholic Church continues to have these requirements of form for a valid marriage; in general, Reformation denominations do not. (This doesn’t mean that Protestants don’t have requirements of form, so to speak – it’s just that they defer these requirements to what the government requires (the couple must be free to marry, they must have a valid marriage license from the state, they must be married by someone recognized by the state to perform the wedding, and they must have witnesses), and they don’t add any additional requirements themselves.)
So, although it might appear that you’re asking a question about ‘consent’, you’re really just asking a question about ‘form’. So, in answer to your question, ‘no’: in order for it to be a valid marriage, there cannot simply be a secret exchange of consent; there are certain prescriptions of form, which define how that consent is exchanged, for a valid civil or Catholic wedding.
Would they, at mutual consent to be man and wife, become one?
That’s the question you asked before. I would answer ‘yes’ – they are validly married at the point that they exchange consent in a valid ceremony, and at that point, are a “one flesh union.”