There is absolutely no way right now that any University, its President, Provost, AD, or any University administrator would receive even minor allegations of abuse or inappropriate contact (let alone an official NCAA waiver/petition alleging abuse/inappropriate action) and would not conduct a formal investigation. That would be the the stupidest decision a University administration could ever make, let alone try a cover-up. The legal, criminal, and financial ramifications are insurmountable.
They would not only conduct a formal investigation, but would either challenge/deny allegations (if found not true) or take appropriate actions against the accused (if found them valid).