That's yet to be determined. The judge ruled that an entirely separate trial will be necessary to determine if Anthropic violated specific copyrights when they downloaded books from pirate websites and what the damages would be if they did so.
So far no court case has ruled downloading to be a violation of copyright. In Sony BMG Music Entertainment v. Tenenbaum and Capitol Records, Inc. v. Thomas-Rasset the courts ruled that downloading and then sharing the content constituted a violation of copyright law. Those are the only two cases I'm aware of where a ruling was made (relevant to this).
The courts need to be very careful with any such ruling because search engines download pirated content all day every day. If the mere act of downloading it violated copyright law then that will break the Internet (as we know it).
The analogy the judge gives is to how Google Books walked the tightrope on copyright: they maintain an archive of all the books for indexing and search purposes, and can display excerpts to help you confirm that's what you're looking for. The excerpts are constrained so you can't read the whole book by scanning the excerpts.
If post-filtering the LLM signal is illegal, shouldn't Google Books archive also be illegal? If not, why not?
And if you believe it should be, understand that the way precedent works, the judge won't be ruling that way without pulling some fire on themselves, because it is not the business of another case to contradict the conclusions of a previous court in a previous case. Copyright law is arbitrary and highly path-dependent because the underlying goal is forever in tension with itself, that goal being providing societal benefit by creating artificial scarcity on something that is, by its nature, not scarce at all.
(Worth noting: Anthropic didn't get off scot-free. The ruling was that the created artifact, the LLM, was a fair-use product, but the way it was created was through massive piracy and Anthropic is liable for that copying).