If the Luftwaffe had a large enough number of Schwalbes during the Normandy campaign, I think they could have stopped the Allies advance. The Germans weren't short on people, and they had plenty (greatly superior) tanks to combat the Allied tanks.
It was Allied Air Superiority that forced the Wehrmacht to move at night, and be strafed and bombed during the day. In my opinion if the Me-262 was around during D-Day (in large enough numbers) it could have stopped, or at least delayed, the Allied invasion. It would have gained air superiority easily.