On a site where I do have an account, the left part of the top bar looks like this:
On SE sites where I don't have an account, the user information and review queue icon is obviously missing, but also the inbox and the achievement dropdowns.
The user avatar, reputation and badges are obviously information tied to this specific site, so it makes sense that they're missing. The same goes for the review queue, as I can't review without creating an account.
But the inbox and the achievement dropdowns are global features. They're the same on every SE site, and they display information from all sites you're active. It doesn't make any sense that they're suddenly missing just because you're looking at a site where you don't have an account.
To me it would make much more sense to always show the inbox and achievement icons on all sites, and to move the "Join this community" banner into the place where the user information usually is.