What do vouches have to do with any of this? You're talking about a subset of the population that no private school is going to touch - because if they do, there go the rest of the paying customers.
If students and their parents have vouchers and a good attitude toward education, the rest will likely fall into place. If established schools didn't want to touch them, as you suggest, I expect new schools would start appearing to fill the gap. However, absent a desire to learn and work, vouchers may not help these kids very much.
There will be a lot of private schools opening practically overnight. They may be in church basements, but they will accept kids who want to learn. The "subset" will probably remain in public schools. Meanwhile because all parents will have a choice of where to send their children, we, the taxpayers, will no longer be held hostage by the teachers' unions. We will also no longer have to build expensive Taj Mahals and probably will not have to pay for busing.