I found a reference which describes the process of connecting Windows Phone 7 to Zimbra, and it merely states setting it up using the WP7 native Outlook client.
Now, this connectivity is obviously not available in the free, open source Collaboration Suite in the standard download package. But is it available to add onto it in any way? I don't want to purchase a full commercial version, since this is just for my personal and family use. I would, however, be fine paying for the connector or add-on or whatever is required just to add this functionality (as long as it was "reasonably priced").