Yes, because the incentive to work would not be as high if you can receive $30k/yr, but only $3/hr working food service. But, if they receive $30k/yr plus $20/hr (or whichever number is appropriate for COL in the province/area), then people are more likely to work - and do so productively. This then encourages economic growth through money changing hands and being taxed.
Minimum wage is great for welfare, but economic well-being is not quite the only goal of minimum wage; it also serves to encourage people to join the workforce over alternatives, and to spur economic activity.