Because the DNS name for a name based site is actually the IP address for the Private Server the two URLs are in reality the same thing. And in /home/httpd/html there are symbolic links pointing to all the sites. Whether or not you want to handle it this way is up to you.
There may be some problems with CGI-scripts that need to write to file since your actually running the secure server under a different user/owner. Basic scripts such as formmail will work properly.