Is it possible that good teachers hang out in the lunchroom and encourage their students to eat? I don’t think it’s fair to so readily dismiss the hypothesis without a good look at the relevant data.
If children aren't eating, the cause is most likely not being able to afford food, or not being provided with food by their parents. If teachers were to have any effect, it would be by giving the children money or food, not "hanging out" and "encouraging" them.