Hi Andy,
It's a best practice for admins who have multiple roles in an organisation, to also have separate accounts for the teaching and administration roles. This is to make sure the user only has the tools enabled that are associated with the role the user has logged in with.
Teacher is normally not a category level role, and it might work. If you don't fancy going into each course and manually enrolling the user as a teacher, you could consider the Upload Users CSV option with the appropriate enrolment field for the courses the user has to be a teacher in.
Info on the Upload Users CSV options can be found in the Moodle Docs: https://docs.moodle.org/36/en/Upload_users