Where the difference is substantive, yes. Proceeding on a description the applicant knows is inaccurate creates a record that is difficult to correct later, and a revised letter is generally easier to obtain than the consequences are to unwind.
Build the revision into the schedule
Tell the employer early that the letter needs to describe actual duties, so the revision happens alongside other onboarding steps rather than at the last moment. If a start date is already fixed, raise that constraint with counsel immediately so the sequence can be planned around it, rather than assuming the letter can be fixed in transit.
Confirm the profession and credential first, then obtain the signed support letter, then decide the venue, and only then give notice and sign a lease. Ask the client for a realistic construction schedule, including likely delays, and compare it to the period the applicant expects to be granted. Review whether any other terms or duties changed and coordinate the lawful start using the actual record. A TN application presented before the underlying evidence exists is not faster; it produces a refusal record that then has to be explained in every later application.