We would like people to see a document library listed on the Quick launch bar even if they do not have permission to the library. We don't want them to be able to access the library, just be able to see that it is there. Is there a way to do this?
You can add a link under Current Navigation section in the Navigation settings page. This will be visible to all users but throws "Access Denied" error if a user doesn't have permissions.
Note this "Navigation" settings available only if publishing feature is enabled.
You can read this article about complete navigation settings.