No. At least two possibilities:
If your linux/unix skills are good you can do this manually using doveadm:
http://wiki2.dovecot.org/Tools/Doveadm/Import
If you want to stay out of MIAB, use an email client to do this:
- Add your MAIB mailserver as an account
- Add your existing server as another account and make sure to fetch all its email
- Copy/move your folders/messages from 2 to 1.