The user then needs to be subscribed to their mailboxes. This must be done logged in as the user - that is hard, I have no way of knowing their password.
This might be easily worked around using the ability of cyrus-SASL to authenticate one set of credentials and authorize access to a different user's resources. I don't think you can use cyradm, as it expects to be an IMAP admin, but you may be able to do it with a simple perl IMAP client.
I've used this trick with mailutil (from the uw-imap project) to great effect when migrating mailboxes from a previous IMAP system.
Craig Ringer