Hi,
This plugin just connect to your smtp, so better way will be to store emails with your smtp account (mandrill, sendgrid or whatever you use).
Or you can do it with form plugin what can store entries in database, but this will not stores emails out of contact form such as registration emails from wordpress.
Anyway there are more email log plugins, which store emails in database, so do exactly what you need.
You can check them https://wordpress.org/plugins/search.php?q=email+log