Harry's idea of dealing with McGonagall involves using the Time-Turner again. This means a version of Harry must leave Mary's Place before Harry and Quirrell begin their elaborate precautions in Mary's Room, and maybe before they even order their food (Ch. 51). Whoops.

Harry's response is correct, assuming McGonagall's Patronus visited after they activated Time-Turner the first time. It means that they can Time-Turn again (somewhere hidden), enter the room before it's sealed by their first versions, wait hidden in the room for first versions to travel in the past (disappear from timeline), then open the room and let Harry meet McGonagall.