Obviously, the intrinsic rewards of learning aren't working in New York's schools, at least not for a lot of children. It may be that the current state of achievement is low enough that desperate measures are called for, and it's worth trying anything. And we don't know whether in this case, motives will complement or compete.
But it is plausible that when students get paid to go to class and show up for tests, they will be even less interested in the work than they would be if no incentives were present. If that happens, the incentive system will make the learning problem worse in the long run, even if it improves achievement in the short run -- unless we're prepared to follow these children through life, giving them a pat on the head, or an M&M or a check every time they learn something new.