On your migration date, all of your mail (even your folders) will be transferred over to your new Google Apps [1] account. It may take a day or so for it all to arrive, but you'll still be able to login into Zimbra at zimbra.humboldt.edu (or your old mail client) to find messages that haven't transferred. See our Migration Information [2]
Links:
[1] http://www.humboldt.edu/its/glossary/5#term40
[2] http://www.humboldt.edu/its/google-move