Yes it's possible. For best results you should shutdown your current services first so that the install of Zimbra doesn't conflict with MySQL, tomcat, postfix, etc.
You should be able to export your contacts to a cvs file and then import them into Zimbra.
As for moving mail I think a program like mailutil from UW can copy from Unix format to IMAP. So you could import mail with that tool.
http://www.washington.edu/pine/man/#mailutil
Not had a chance to try this yet but conceptually it should work. If you already have IMAP access then check out the imap-sync thread which explains how to do a simple IMAP copy of your mail into the Zimbra system.