Are there any notifications (mail & Global Inbox) for unregistered users?
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As long as the unregistered user has the cookie, then they will get to see updates in their Global Inbox. Because they aren't registered (and thus have no potential for associations), the inbox will only show activity for the current site.
Unregistered users I believe also still have the permission to opt into getting emailed on updates. I'm not fully certain on this point, but I'm pretty sure they have the option, since they must specify an email.