I'm sure someone might try to argue that the AI generated song might constitute something like an "AI cover", but I would disagree. The issue is the creative act. Humans are creative and can emulate or even "cover" a song as close as possible and it's still largely protected as long as you don't explicitly mislabel it as the original or attempt to pass it as the original ("original" in this sense being the rights holder and owner).

An AI generated song, I would argue, is not really "creative" in the same sense. It's not even really a cover. It's a generated output built on the original IP to a degree that is well beyond human capacity because it's not human at all. It's machine generation and not artistic creation. People like to conflate the two, but they're being wilfully ignorant of the clear differences between the two. Prompting an AI model to output something is not the same thing as making it oneself. The only human element of an AI song is the prompt and not the output.

It's more likely that an AI song should and will be treated in the same way as clearing a sample in hip-hop, for example, even though it's also different in important ways.