You should be able to edit Universal Email on any page that it is applied to regardless of weather or not a template is applied to the page. The server side code that UE produces will be above the top html on the page so it should have no effect on any template part of the page.
In UE4 if you choose to edit the contents of the message from within the interface you will be making edits to a templated page with editable regions in it. What is the process you are going through to add and edit the emails and what is the file that you have to detach from the template?