Yes.
Local delivery uses LMTP and not SMTP. It *should* deliver to itself, even if you don't have an MX records.
For example, I have a test machine set up on my mac. No DNS whatsoever. The useraccount is
admin@john-holders-mac.local
If I send mail to that, Zimbra uses LMTP to deliver it, and it goes through.
Take a look at your /var/log/zimbra.log
That's the Postfix log. If there's something fishy, it's there.
Good luck,
john