That was the impression that I had gotten... however, my experience seems to differ.
The IP address I want assigned to zimbra, is the only one present in my hosts file and is the A record in DNS for both mail.mydomain .com and mydomain .com.
I even went so far as to take down the virtual interface while zimbra installed. Allowed zimbra to install, restarted the network to bring both IPs up - and apache complained about the socket being taken on my second IP.
This is a clean install of Ubuntu, the only thing installed on it is MySQL, Apache, Webmin and Zimbra. Here's the smoking gun:
It seems regardless of what is set in hosts or DNS, it attempts to bind to all listening addresses, i.e. *:www
root@mail:~# lsof -i :80
COMMAND PID USER FD TYPE DEVICE SIZE NODE NAME
java 17002 zimbra 74u IPv6 1501558 TCP *:www (LISTEN)
Where/How can I change this behavior?