POP aggregation in version 4.5
Version 4.5 of Zimbra will allow you to do POP aggregation -- downloading mail from your remote system's INBOX into a folder on your Zimbra system. You can either leave the messages on the remote system or have them deleted once they've been copied to the local Zimbra server. Once they've been POPped from the remote server, there is no traffic to the remote POP server until the next time you want to fetch the mail, at which time only the new messages are retrieved.
(Note that Zimbra is not a web front end to a remote email system -- it's also a mail store, and you can't run Zimbra in a front-end-only manner.)