The officials who pick kids to go to supposedly better schools, will pick the kids that are easiest to deal with. Kids that are in bad conditions, but not overly bad. Kids that are pretty well behaved. The kids that are in extremely bad conditions and act out more, will get left behind and yes, they will be minorities.
By allowing students and parent the ability to choose where their child goes to school, the obviously inferior inner city schools are not the only place where a child may recieve an education. They would have the option of attending another school. Since the inner city schools are often host the majority of minorities, giving these racial minorities the option to attend another school would not only allow them a better education, but promote diversity in the school of their choice.
Vouchers are handed out to help all students of all races choose the schools they want their children to go and to push schools to compete for students. There is no reason to believe that letting parents choose where to send children for schooling will result in more discrimination than any other choice made by individuals.
No, school vouchers would not increase racial discrimination, because students would be able to have options for their education. Vouchers would be most helpful to poor minorities, because they could use the money to get out of the inner city schools and into private schools. The private schools would happily take their money.
I think overall as long as the vouchers are handed out fairly then they do not increase racial discrimination, if everyone has a equal chance at obtaining a voucher then anyone regardless of race can attend a private school and there can be no claims that they increase racial discrimination.