Sharepoint: public welcome pages, private sub-sites

Is it possible to create public welcome pages for private sub-sites? The welcome page would contain links to the private sub-site, but be accessible through permissions. I have the site hierarchy based on the structure of our company, so there are nested sub-sites. Also, I would like to have a public announcements folder (that would be on the welcome page) and a private announcements folder (on the internal sub-site). Can this be done?