Not by itself. Contracting arrangements are not prohibited across the board. What matters is whether the arrangement still shows a qualifying listed profession, an accepted credential, and prearranged professional employment for temporary entry, and whether any ownership interest raises the self-employment bar.
Structure is assessed on its facts
Complex contracting arrangements belong with counsel rather than a checklist, because the answer depends on who engages whom, who directs the work, and what the professional's relationship is to the entity receiving the services. Assuming every contractor is excluded is wrong; assuming any contract will do is equally wrong. The agreement itself has to be read.
Listed teaching professions turn on the nature of the appointment and the credential behind it. Use the institution’s actual credential status and the profession’s particular requirements. TN requires Canadian or Mexican citizenship, not Canadian permanent residence, plus prearranged professional work in the United States for a U.S. entity through a U.S. or foreign employer. TN is limited to a citizen of Canada or Mexico who has prearranged duties in a listed profession and meets that profession's rule. The first review should match each stated duty to the listed profession before any title is polished.