I found this article somewhat helpful. I haven't solved my problems yet, but it offers some things to try or at least an explanation that it doesn't always work out of the box for everyone.
http://buzztoneorg.project.buzztone.com.au/contact-form-7-email-issues/
I've got CF7 installed on another site and it works perfectly. I've never seen anything showing it being sent from WordPress (on either site) except when I tried not putting anything in the From field to see what happened.
I actually have a bigger issue in that my client is not receiving the e-mails at their domain ... I'm going to start a new thread for that.