Well, again, if you're a parent, you're giving to the school your kid goes to regardless, and if you're really really wealthy, it's going to be a large donation. If you're not a parent, then you're probably not donating to the local school anyway, because you have the entire universe of possible charitable contributions open to you, and there's probably something you care more about than your neighbors' annoying kids.
Maybe the amount that the parents give will vary depending on the size of the deduction available, but since a donation effectively feels like a donation to your own flesh and blood, I don't think it would be much of a factor.
But yes, if you want to attract donations from the really really wealthy to poor public schools, then there's no doubt that a double deduction would do it.