Hi
Welcome to the forums.
You do realise that Zimbra is a complete solution for email, don't you? You don't install it on your webserver, it installs in it's own directory and it includes it's own servers - Tomcat, MySQL, Postfix as well as anti-spam and anti-virus software.
I'm not a user of Thunderbird and I might be totally off the mark here but, IIRC, you can access a .pst file with that and I think you should be able to copy the mails to a Zimbra account. If that's not correct then I'm sure a more experienced Thunderbird user will correct me.
To answer your question, yes the import tool is for the Network Edition.
HTH