Yep. This is exactly what happens when you set a minimum wage, because the actual minimum wage will always be $0. So you’re not effectively setting a minimum wage, you’re forbidding the people who would work between $0 - (whatever minimum wage you set) to work.

The only sensible minimum wage is no minimum wage. Anything else causes great harm to the weakest in our societies, often catastrophic amounts of harm in the form of perpetual unemployment.