Yes, you can control whether formatting is retained for pasted text into the drag-and-drop editor. This is a setting on the individual administrator record.
1. Click Settings icon > select User Management.
2. Locate and click Account Administrators (left column). If you are a Site Administrator, click the Site Administrators tile instead.
3. Locate your administrator record and click 'Edit' button (right side).
4. On the opened record, scroll to the bottom of the page.
5. Locate and check "strip all formatting when copying from clipboard".
6. Click Save.
If you paste text from an external source (and do not choose to paste as plain text into the editor) the styling from the external source will override any styling you have set on your email template.