No. A visitor admission permits a visit, not employment, and no general rule authorizes work simply because an application or petition has been filed. Work may begin only once TN status is effective or TN admission has been granted, depending on the route.
Keep the visitor admission and the work question separate
Two different permissions are in play. The visitor admission covers presence for a visit until its end date. Authorization to perform the professional work comes only from TN status or admission in that classification. Confusing the two is what leads to an early start that surfaces later, at a renewal, a new entry, or a change of employer, when the record is examined more closely.
Each TN case turns on prearranged professional employment with identified terms. Work with the employer to describe the genuine duties and engagement at an appropriate level. Federal law requires nurses and several other health-care occupations to present a health-care worker certification at admission; an officer at the port of entry will ask for it, and a pending application is not a certification. A polished title or a Canadian employer address does not, by itself, establish either fact. Once the employer confirms the assignment, a Canadian may generally present the case at a port of entry or the US employer may file Form I-129.