If you have access to another email account (for example, the mail for your department), this account will be moved on the same day that their owner is moved to Google. An account owner is the person who is primarily responsible for the account. In some cases, account owners have changed but were never updated. If this is the case, the account you access may move to Google before or after you move.
If your mail does move ahead of you (e.g., you are no longer getting mail in Google), you could log in to Google Apps  (from the webmail login page) to access that mail in the interim.
If you move to Google and the mail for that account is still going to Zimbra, you should email the Technology Help Desk  at firstname.lastname@example.org  and ask them to move that account. We'll be a little busy helping folks move, so if we can't get that account moved right away, you can still login to Zimbra to check that mail.