We currently use Zimbra 8.0.5-FOSS using both IPv4 and IPv6 without any issues.
It may be considered "Beta" still, but it works just fine, had it running using ipv6 for about 7 months now. Activating it is actually a lot easier than you'd think though.
Ensure your AAAA DNS records are set correctly and just run this Zimbra command as zimbra user:
And well, that's pretty much it. It should now "just work".
zmprov ms `zmhostname` zimbraIPMode both; libexec/zmiptool; zmcontrol restart