Only if the credential already satisfies the listing. A licence application will not complete in that window, so the realistic options are to ask the employer to wait, to start in a Canadian role, or to decline.
Say early that the date will not hold
Raising a foreseeable delay in week one leaves more room to revise the start date than disclosing it in week six. If the plan depends on a provincial licence, the timetable belongs to the regulator, and the assessment, examinations and experience review are measured in months. Telling the firm now, with a realistic date and an interim proposal, allows it to evaluate the available options. A workable interim can be a contract with the employer's Canadian affiliate if it has one, or a short consulting arrangement performed from Ontario, which raises tax questions but no status question because the work is not performed in the United States. What does not work is arriving on a visitor admission and beginning the job while the paperwork catches up.
Hypothetical example: a geologist is offered a field-supervision role that begins when drilling starts in April. The first review produces a backwards calendar for the employer letter, degree records, entry request and any licensing inquiry. The date that matters is the first day of professional services in the United States, not the day the offer is signed. If the project schedule moves forward, the employer must decide whether to delay deployment or use staff already authorized for the work. Entering as a visitor to begin field duties while waiting for documents is not a valid bridge.