http://www.cbsnews.com/news/pennsylvania-school-cafeteria-worker-quits-over-lunch-shaming-policy/Schools refuses lunches for children with overdue lunch bills. Since instituting the policy the lunch program debt has gone from a fluctuating 60k$-100k$ down to 20k$. So it's undoubtedly effective.
A second aspect to consider is that children who are expected to pay for lunch have been deemed by the state financially able to, so this excludes the incredibly poor who have their lunches paid for in full. This is really just effecting people who pay a partial total for lunches or full price for lunches, which isn't to say they can strictly afford it as the state's formulas are imperfect.
More generally should a state entity ever practice debt collection by involving children? An alternate example that seems socially exceptable is late fees on public library rentals, children aren't allowed to rent more until they pay, but books =/= food.
In my opinion this is abhorrent, and potentially a situation for a bully to latch on to. As someone who lives with a teacher I know the terrible response rates that parents have to calls or materials sent home, sadly that's the only way. The rock and a hard place here is that most parents are under-involved in their children's education so issues like this fall way off their radar. (no i dont have stats, im drawing on anecdotal experience)