Hi AB1-AB1,
Does your selected list in MailChimp for WP > Checkboxes require any other fields besides just EMAIL?
Also, you should use a checkboxes named "mc4wp-subscribe" in order for the plugin to kick in. That's probably why the plugin isn't sending anything to MailChimp.
To render the checkbox, please use the simple to use [mc4wp_checkbox "Label text"] value in your CF7 mark-up.
Hope that helps. If not, let me know!