No shell access
I don't have shell access on my server (cpanel admin with the ssh option disabled). Am I just out of luck? With no root access (my lowest level of access is home/username) could I intall it in the non-public base directory and install via raw ftp command? Just thinking out loud here.
Getting this to install would be a pretty large undertaking - you'd have to convince rpm to install in a different directory than /opt/zimbra.
Once that's done, you would have a real problem running the system, since you won't be able to bind to any privileged ports - which means, among other things, that you won't be able to receive mail.
Come to think of it, rpm won't let you install anything if you're not root - so you'll have to download the source, and try to make the dev-install targets work by changing the destination paths. You still won't be able to bind to port 25, 80, 443, 389, etc..