If only poor people bought food, and if the poor people were going to be suddenly dramatically better off, and if there were no price competition between the suppliers of food to poor people, then yes, that would happen.

But as it is, food is sold to a wide variety of people, who are varyingly price conscious, the poor people will be better off, but mostly this will replace existing payments, and if someone tries to ramp up the price of their cheap food then they will be undercut by a rival.