The answer is NO if an April 2008 study of the Florida McKay Scholarship Program is any indication. Public school students who don't take advantage of the scholarships created by House Bill 3393 will also likely benefit.
A Manhattan Institute for Policy Research report evaluates the impact of the Florida McKay Scholarship Program for disabled students on the academic performance of the students who remain in the public school system. Oklahoma's Lindsey Nicole Henry Scholarships for Students with Disabilities Program (HB 3393) is modeled on the McKay program. The McKay Scholarship is the oldest program of its type and the most studied.
The report summary states: "The report evaluates the impact of Florida’s McKay Scholarship Program for Students with Disabilities ... on the achievement of disabled students who remain in their local public schools. Using data on public school students in Florida from 2000-01 through 2004-05, the authors found that reading and math test scores of students who were eligible for McKay vouchers but remained in the public schools improved substantially, even as private school alternatives became more available. The largest category of disabled students—those with Specific Learning Disability, a mild form of disability, accounting for 8.5 percent of all students in Florida—enjoyed the greatest gains. The academic proficiency of students diagnosed with more severe disabilities was neither helped nor harmed."