If anybody else stumbles on this, here is the answer i worked out:
Even for multi-site, there is only one users table in your WP database. So it does not matter where they register. However, unless you configure it properly when they sign up, the user will be “tagged” to the site that they first registered on, and only on that site. There are many ways to configure to do what I wanted above, and I ended up using a plugin called Multi User Sync.
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