Hello Sam,
We don't do this automatically, but you could possibly create a workflow to check on Sent Emails associated with an Email Send with a certain template. Then you could send a CRM email to the User whose Contact received the email. However, I wouldn't recommend this; it could take a toll on your CRM if you send out a lot of emails this workflow will need to process a lot of data to run. Additionally, this method would send the User 100 emails if they had 100 Contacts they owned that got the email. If you choose to use this method, you'll want to monitor your CRM's performance.
I apologize for any inconvenience. Please let us know if you have questions and thanks for using the forum!