Just finished this past weekend. A couple of things I ran into that I wanted to put out there in case other do too.
My first hiccup was with the License check. For some reason my content filter on my firewall was blocking the check. After resolving that Zimbra support gave me a command to check if I can hit the license server.
su - zimbra
It should reply OK.
It might be a good idea to check this first. Save the headache of troubleshooting after the fact.
The next hiccup was pax was not installed. When it did the checks for required applications this came up. Support was kind of surprised but said it was required for 8.0.6 to run properly.
apt-get install pax
That did the trick. After that the rest was smooth sailing.
I am probably over cautious but I ran both a zimbra backup as well as a full backup using my sporty PHD Virtual backup software before going ahead with the install.