That's the thing though isn't it? If the productivity goes up then that's great as the employer gets more value and the employee gets the higher wage. If just the wage goes up though, then the employer will increase the price of their products to offset the increase in costs, so relatively speaking no one is better off.
http://www.nber.org/papers/w6127 seems to suggest that in net terms, minimum wages don't do anything to really help alleviate poverty. If you can make people more productive however, that will do wonders.