Nor can it be an entity to sign anything.
I assume the "not-copyrightable" issue, doesn't in anyway interfere with the rights trying to be protected by the CLA, but IANAL ..
I assume they've explicitly told it not to sign things (perhaps, because they don't want a sniff of their bot agreeing to things on behalf of MSFT).
We do know that LLMs will happily reproduce something from their training set and that is a clear copyright violation. So it can't be that everything they produce is public domain.
I can't remember the specific case now, but it has been ruled in the past, that you need human-novelty, and there was a case recently that confirmed this that involved LLMs.