I don't think this is a fair analogy. Unfortunately, analogy breaks down because the technology is unprecedented. So, to answer directly, no the poet cannot copyright the unique meter, but, no, machine learning is not that.
If you need an analogy, think copy machine, not human learning. An LLM can only regurgitate that which it has seen before. Absent the poet, the other poets can still make other poetry, but the LLM literally cannot make poetry that it has not seen before. If it produces a poem with that unique meter then it definitely copied that poet, and was not "inspired by" the poetry. If you wrote poetry inspired by EE Cummings your process for doing that would be very different from an LLM's, which would programmatically use his material.