No! What hurts the poor is a deranged immigration policy
Hah! Thank you for illustrating why rational debate is almost impossible today.
Yes! Minimum wage laws hurt the poor.
Yes! Insane immigration policies hurt the poor.
Those two harms are not exclusive of each other. You may rightly debate which of those two bad policies causes more harm. OTOH, to say that either one is NOT harmful, because the other one exists is consistent neither with logic nor with observed fact.
Re: “Those two harms are not exclusive of each other.”
If there was a massive labor shortage, wages would skyrocket, businesses would be much better managed, and labor saving capital investment would increase.
Instead, thousands of new businesses are created every year in the USA predicated only on the fact that wages are stagnant or falling.
Personally, I support a $15 per hour minimum wage, because it absolutely destroys the rationale for massive immigration.