The short answer again, maybe.

You might get it working but I wouldn't guarantee it.
My recommendation would be to install Zimbra on CentOS 4.4, it's built from the Redhat 4 source and RHEL4 is the recommended o/s for the Network Edition of Zimbra. I use CentOS without problems as do some other members of the forum. It's a server operating system and designed to run this type of application.