I think you are not quite seeing this correctly. You do not become "government funded" simply by accepting one student with a voucher. No court will see it that way.
And, how will private schools be able to maintain private school admissions standards? Won't they be "discriminating" if they don't take a student with "special needs" or with a "disciplinary record"?
This simply just will not happen. Like I said, most private schools will probably consult an attorney before they even accept a voucher student. If the school "changed" some rules because of whatever, then it would go broke, because parents would just take their kids out and send them to another private school that didn't accept voucher students.
If ANY court rules that once a private school accepts vouchers, its no longer private accept that they are privately funded, then no private school will accept vouchers. Its that simple. You are forgeting that it is the school's choice to take vouchers. No court will rule that private schools have to accept voucher students. There is as much basis for that as there would be for saying private companies have to hire any former government employee.