No, if you send your kids to private school you still pay public school tax. However, when people get vouchers I believe they come out of the school tax fund.
I hate vouchers too though, for what it's worth. It sends a terrible message to your child of "if something needs improvement, just walk away instead of trying to fix it." Not to mention that unless you are in a city it's totally farkin' useless - the only thing where I grew up that wasn't public was a Catholic school and I don't understand the concept of sending your kids to a school that is of a religion you don't practice (although apparently many parents do
.)