That is a great question. On a technical level, Plato's dialogues are not poetry, since there is a difference between Plato and say the works of Aristophanes or Sophocles. For instance, the later are in meter, where as Plato is not. However, Plato wrote a lot! And there are poetic elements in his dialogues. So, in this sense, parts of his work may be considered "poetic." However, from a larger perspective, his works are prose. Now we need to ask the question of why Plato does this, when he speaks out against poetry. The answer is, because he is a master at dialectics, a true seeker of wisdom. Therefore, he will not be lead astray, like the masses, by poetry. So, while the masses should not engage in poetry, but one who is a philosopher may do so.
Yes, I think Platonic / Socratic dialogue, depending on translation, can be made to read like a kind of poetry. If it is written by one author after the conversation has taken place and reassembled with metaphor and imagery in mind, it can certainly be read as a double-voice poem.
It certainly is in Cormac McCarthy's The Road, which is a kind of mobile Socratic seminar, a walking discourse. Since they only have each other to talk, the father and son resort to a Socratic method of poetic dialogue. The boys asks, and the father answers. Toward the end, the boy arrives at a conclusion, and the father answers.
The conversations the father and son have keep the fire going as much as anything. They are crafted so beautifully. McCarthy omits conventions (commas, quotations, and sometimes question marks) because they intrude on the poetry-prose. He's a poet novelist, and he's got a lot of e.e. cummings in him. He wants to expose the words in their bare beauty.
McCarthy prefaces a lot of his would-be questions with "and" or "but," turning them from questions into statements. Usually, these would-be questions are at the end of a back-and-forth discussion and are used usually by the boy for clarification. Most of the time the father simply says, "yes" to agree.
Look at the two passages below: the first is from The Republic and the second from The Road. They are written in the same style as a "Call" and "Response" song style used in many religious ceremonies, hymns, and blues songs.
There is a real danger, he said.
Then we must have no more of them.
Another and a nobler strain must be composed and sung by us.
And shall we proceed to get rid of the weepings and wailings of famous men?
Although I wouldn't call it a poem by itself, the following conversation from the Road devolves into a kind of similar poem:
Why do they have to do that?
I dont know.
Are they going to eat them?
I dont know.
They're going to eat them, arent they?
And we couldnt help them because then they'd eat us too.
And that's why we couldnt help them.