No this is not possible as we are unable to set up a copy of all outgoing emails to be sent to your email address.
You can however set up an email forward of all emails sent from your email domain to be copied into your CRM account - this is done via your email server where a copy of all incoming mail received is automatically sent to your CRM account dropbox email address where you will see a copy of all email received on the Dashboard.
To read more about this please click here.