With my Sendmail / Dovecot / Squirrelmail setup, I am using Procmail to distribute user mail to specific directories. It would make sense, you need to tell sendmail how to deliver the incoming mail instead of letting it sit in /var/spool/mail. You might be able to setup Dovecot to read mail out of there as well.
I highly recommend you read the Sendmail Cookbook and the Big Bat Sendmail book as well. It will enlighten you with the power of Sendmail. I wonder how long it will be before Oreilly comes out with a book on Dovecot?