I am going through the same process and have encountered the same issue. I've tried:
Deleting the template. Still received email as the agent who replied to the ticket. The content was only the note history.
Restoring the template but leaving "enabled" unchecked. Still received email as the agent who replied to the ticket. The content was only the note history.
With the template created but "enabled" unchecked and "add note history" unchecked, no contents in the "text" body of the email template. Still received email as the agent who replied to the ticket. The content was only the note history.
It seems that no matter what, even without a template, at a minimum, the system generates an email sent to the agent with the note history.