If active, the SubSpace navigation is always displayed - regardless of the current space or the login state of the user.
The only exception is the Administration.
Permissions are handled as follows by the SubSpace Navigation:
If a navigation element is not displayed for the user, any element below it in the hierarchy will not be visible either.
This does not have any effect on the content the user is allowed to see in Confluence. Even if a child element is not displayed to the user, as long as they are allowed to access that page/space, they can still view it, e.g. using the Confluence search.