It's not Growl that needs to “work in” Zimbra; it's Zimbra that needs
to talk to Growl. Growl just listens for notifications; it doesn't go
into other applications and pull them out.
I did some searching, and you need to be using Zimbra Desktop beta 3
or later:
<http://www.zimbrablog.com/blog/archives/2008/07/zimbra-desktop-beta-3s-new-features.html
>
Using the website alone won't work, and older betas and alphas may not
work, either.
Also, you need to turn it on in Zimbra's Preferences. It's the fourth
checkbox in the list of notification methods.
So far, it's still downloading all my old email, and it definitely
does not post new-mail notifications while it's doing that. So, I'll
have to test it later, after it finishes with the old stuff.