Not likely. QNS means the candidate was qualified with a nomination. Being "qualified" implies that the candidate met the academic standards. My understanding is that Prep School is intended for those who are not academically ready but have strong leadership or other qualities that the academy is interested in. It is essentially a year to improve test scores and become prepared for the academic challenges of West Point.
The path forward if you get the TWE is to execute Plan B and reapply next year.