I use both the Outlook connector and the web mail interface to Zimbra, and I've setup fetching other IMAP/POP mail accounts in both places. In particular, I've setup the POP accounts in Outlook 2003 so that they fetch emails directly into the Zimbra account Inbox and delete emails on the POP server when they are cleared out of Outlook's Trash. It all seems to work OK, although occasionally deleted items get out of sync.
But do I really need to fetch external POP accounts in Outlook at all, if I've already done that in Zimbra? In other words, when the Outlook connector synchronizes with the Zimbra server, does that automatically start the POP fetch process for the external accounts I defined in the Web interface, just as if I had clicked the "Get Mail" button in the Web interface?