Sure, many work may work in construction at the lowest end but that not the limiting factor for if construction actually happens.
You don’t need 10,000 framers and day labourers you need electricians, plumbers, cabinetry makers, engineers, architects, gas fitters, HVAC technicians, etc.
Almost all of those people need schooling and certification and the lack of those people as well as the permitting process and municipal rezoning process is what’s preventing housing from being built fast enough.
Bringing over a million day laborers is not going to help solve the housing crisis, it will stress it.