Non-admin users can see the Admin bookmarks block, but not the contents.
When the Admin bookmarks block is added to Site Home with 'Display throughout the entire site', both teacher and student roles can see the block when they Turn editing on on an appropriate page (e.g. my Home, or a course homepage).
They can also modify the configuration of the block on that page.
Presumably other non-admin roles can also see the block; we haven't tested for that.