Hehe, dijicji2 summed it up succinctly. No, would be the easy and 99% answer. The extra 1% is that the FOSS version is open source for a reason and you could swipe all that code and put it to your needs. Of course you would need to know a hefty amount of HTML, CSS, AJAX, and all the non web programming to rebuild the server to fit your situation. At that point why not write your own?
Basically with Zimbra you have customized Postfix and all the software Zimbra uses. It's all canned binaries built for each system the test on, or the source you can compile yourself. The software that Zimbra uses to function does not run off the standard packages which Ubuntu, Redhat, and others keep in repositories, thus the web client is not able to function off of them.
Simple answer is no. Complicated (very) answer is, well maybe.
Mail | Dell 2950III | 2x Quad Core 5420 | 8gb RAM | 6x 146gb SAS RAID 0+1 | Red Hat 5.3 | Zimbra 6.0.10 Network Edition
Test | VMware ESXi Whitebox | Phenom II Black 3.2ghz | 12gb RAM | 6x 1tb SATA RAID 0+1 | CentOS 5.4 | FOSS, Not in use now