Yes, as an employee of a treaty enterprise. The employee must hold the treaty nationality and be coming in an executive or supervisory role, or to perform duties requiring essential skills.
The investment belongs to the enterprise, not to the employee
The employee route exists precisely because a qualifying enterprise needs people. The conditions are different from the investor's. The employee must have the nationality of the treaty country, which for a Canadian-owned American enterprise means Canadian citizenship, and permanent residence in Canada does not satisfy it whatever the person's length of residence.
The employee must then fit one of two bases. Executive or supervisory employees are assessed on the authority and responsibility of the position: whether the person directs the enterprise or a major component, controls other supervisory staff, and exercises discretionary decision-making. Essential-skills employees are assessed on the specialisation of their skills and the need for them.
The employer must also continue to qualify as a treaty enterprise. None of this asks the machinist for capital, and an employee who is asked to invest should question why.