Yes, it's two-fold: 1. Those in private school do not have to be funded by the state, and so, given a finite budget, the average funding per child in public sc

Yes, it's two-fold: 1. Those in private school do not have to be funded by the state, and so, given a finite budget, the average funding per child in public school goes up. 2. (Your point, if I understood correctly, and which I hadn't considered...) The tax take from private school fees indirectly helps fund the public schools. Without that tax income, the education budget (or some other public spending) would necessarily go down.