No. The TN entry for teachers is limited to colleges, seminaries and universities. A school-district or private secondary-school position falls outside the profession list even when the teacher's qualifications are excellent.
The list names the institution, not the skill
The TN profession list is closed: if the occupation and workplace are not described in Appendix 2, the classification is unavailable regardless of how strong the candidate is. The teacher entry names three kinds of institution and stops there. A Sainte-Anne-de-la-Pérade science teacher with a bachelor of education and ten years in a secondary classroom is fully qualified as a teacher and still cannot use TN for a district job, because the entry does not describe that workplace.
The same person can use TN for a community-college post, because the credential requirement is only a baccalaureate. If a district really wants the teacher, the district must look at other employment classifications with their own petition, wage and quota conditions, and should be told early that TN is not a shortcut. Presenting a secondary-school job as college teaching because a college board administers the school is a misrepresentation, not a technique.