1) Doing that wouldn't be fairly described as "downloading Twitters database".
2) Given the scale of Twitter, there's no way that would be fairly described as downloading a "massive portion" of Twitter.
3) As you say, there's no reason they would be doing that. It's certainly not needed (or even helpful) for launching something like Substack Notes.
4) Just as a matter of how networking and modern cloud architectures work, it would be a bit surprising if the IP ranges that scraping requests were made from would be the same as the ones serving up content on Substack's frontend. It could happen I suppose, but...it'd be weird, even if you weren't trying to make the requests from unrelated IPs (which...you probably would try and do).
5) Elements of the block have nothing to do with IP addresses or domain names at all, eg, the block on results when even searching for the word "substack" (but hilariously, not when searching for common mispellings), or the block on searching for posts authored by Taibbi.
6) Substack has denied doing any such thing, and frankly, their credibility is currently significantly higher than Musk's.
It's certainly possible Substack was doing something akin to scraping which via a game of telephone ended up as Musk's claim, but... I wouldn't bet money on it.