Am I correct that, in terms of conversation, "converse" can in no way be used as a noun?

The word "Converse" can certainly be used as a noun in other applications of English, but saying anything like that a participant in a conversation "had converse" is surely out of the question?

When you converse, you are having a conversation, or have a conversation (participation implies ownership), and afterward, you have conversed, and have had a conversation. There is - to me - no conceivable way to have or have had a "converse". Or, e.g. "your converse is heard in conversation". This can only be when you are discussing noun converses.

Solution 1:

I wouldn't say it's "out of the question", but it's certainly out of this era. I have never heard converse used this way and it would certainly confuse many people.

But it was used like that:

archaic
Conversation.

• ‘his converse at such seasons was always elevating’
• ‘it will be difficult in these converses not to talk of secular matter’
  _{Oxford Dictionaries}

I was able to find an NGram that mostly avoids false positives. As you can see, the usage has been declining:

Looking at the usage behind the graph (to weed out the false positives), it seems like usage stopped for the most part before 1900. OED.com specifically has this definition of converse listed as "poetic or rhetorical", which is why there are some usages well beyond 1900.

Solution 2:

In the sense related to conversations, you will find examples of "to hold converse" and "held converse" but I believe these to be either mostly archaic or, else, narrow uses within Biblical or spiritual (i.e., in the sense of communicating with spirits) contexts.

So you'll see things like, "God held converse with man, that man might learn to..." for example. If I were to encounter this in the wild in some other context, I would assume the writer was deliberately trying to evoke some connection with these spiritual uses.

Used as a noun, converse also means "the opposite; e.g., However, the converse of this theory may also be true." (Cambridge Dictionary)

Solution 3:

You don't have a converse. That is out of the question. But you 'have converse', at least if you are an 18th Century Puritan.

It would mean that you have ongoing or continual conversations, at least as it appears in laws of that time.

"It is treason to have converse with those known as Ranters" does not mean you cannot talk to them on the street once in while, but if you are in contact to a high degree, that is treason.