Is it legal for a school to pay students to do schoolwork?

No, to offer money as an incentive for students to do their homework is not illegal. 

It is NOT illegal, if that's the question.  This would be STATE law, not Federal, so if you want citations, WHERE?

In MY State there is case law regarding incentives for children to do homework.  It involved an Ivy League School which was concerned about incentives and keeping its rating.  The "incentives" ended up being cash for grades (not homework), and it was ruled to be illegal.

My educated guess would be that the law does NOT address this issue (either pro or con) in the vast majority of States.

Before you demand "codes or laws" (how do you think a code would be involved in this situation"), POST WHERE.  No one is going to post every "code and law" internationally.

I can't imagine why it would possibly be considered illegal.

I can't think of any law that prohibits paying students to do homework

or

that prohibits schools from paying students to do homework.

I attended a school

that paid me to do cleanup chores.

I don't see why doing homework would be different, legally speaking.

That's not illegal, no, just stupid. That's why you never see schools do it, what with their whole point being to stamp out stupid.

If they're a private schoo then MAYBE? Definitely not if public.