No. The Mexican citizen route generally requires a TN visa regardless of Canadian residence, because the distinction is based on citizenship. Canadian residence may affect logistics, such as which consular post is convenient, but it does not remove the visa requirement or substitute for it.
Keep citizenship and residence separate in planning
Treat residence in Canada as a logistical fact, not an eligibility factor. The underlying TN criteria, profession match, prearranged employment, and temporary purpose, apply the same way regardless of address. What changes is the sequence: a consular visa application generally precedes any attempt to seek admission.
Confirm this distinction early with the applicant so expectations about timing and required steps match the actual process rather than assumptions carried over from a Canadian citizen colleague's experience. Write the sequence down for the applicant so expectations match the actual process rather than a colleague's experience. Residence in Canada is a logistical fact rather than an eligibility factor: the underlying criteria of profession match, prearranged employment, and temporary purpose apply the same way regardless of address.
What changes is the order, since a Mexican citizen generally applies for a visa at a consular post before seeking admission, while a Canadian citizen generally does not. Confirm the distinction at the first meeting, because a plan built on the wrong sequence usually surfaces when an appointment cannot be booked in the time available. Check the passport rather than the address.