Depends on the underlying OS as I mentioned.
There will be some sort of switchover which will require downtime if you did a P2V, it would usually be recommended to stop application services for the most smooth conversion.
Not sure what you mean with your last question,
The alternative to a P2V would be some process native to Zimbra - such as deploying a new VM, building up an instance of Zimbra, then migrating mailboxes over from old physical to new virtual.
Is the mailbox data on some form of external SAN/NAS storage?
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