No, you cannot launder copyright through an LLM. It's the same for both images, video, and code; and that question is independent of whether or not it's legal to train the LLM on copyrighted data. The LLM training gets to be fair use, but fair use is not transitive. Infringement reaches through the LLM to get at any outputs which are substantially similar to the original no matter how many fair uses you put in the middle.