Possibly, with premium processing and a file that is already complete, since a Canadian citizen can apply for admission at a port of entry once the petition is approved. The evidence assembly and the qualifying-year check are the parts most likely to slip.
Assemble first, file once, then travel
The adjudication step is predictable: an individual L-1B petition with premium processing receives a decision within the published premium window, and a Canadian citizen then presents the approval notice at a port of entry without a consular appointment. Six weeks can therefore accommodate the government's part. The plant's part is where the time goes.
Procedure records must be pulled from quality systems and organized, the engineering manager's comparison must be written, and the payroll for the qualifying year must be checked for U.S. visits that might interrupt the continuous year. If the parent has already tried the blanket and been refused, the petition must also explain that history.
A request for evidence adds weeks and usually targets the specialized-knowledge showing, so it is worth over-documenting the first time. Tell the U.S. plant the mobilization date depends on approval, and do not ship his tools before the notice arrives.