Teachers are not feeding kids in statistically significant volumes. Schools are, and there might be correlations.
Likely untrue, given a few moments search. For example, "On average, teachers spend $37 a month and principals spend $59 a month for food for their students." [1].
There's lots more data on teachers feeding kids in perhaps causal amounts.
[1] http://neatoday.org/2013/09/10/report-teachers-spend-37-ever...
Given the strong correlation between some breakfast vs none, and school performance, it would not take much to affect the outcomes by feeding hungry kids little snacks.