No, it wouldn't. "Sweat of the brow" applies to collections of facts whose compilation required effort. "Life's work" is a superset of that. Originality and creativity, which are required to copyright something, are also work.
However, LLMs do sometimes output training data almost 1:1 without sufficient transformation, and these cases may be problematic if they could reduce the market for the original copyright owner. For example, if prompting an LLM with "Translate the first chapter of {book} from American English to British English" reliably did what the user asked, perhaps no one would have a reason to buy the book directly from the author.
[1] https://fingfx.thomsonreuters.com/gfx/legaldocs/jnvwzqxzbpw/...
And OP's contention is obtaining the training material and using it in training requires making unauthorized copies. That's the infringement; training, not inference.
Furthermore inference indirectly affects the market for the artist's future work. Don't need the writers and artists the LLM trained on anymore, when it can do similar work for free.