The LW had many aircraft in service in June 1944, very few were seen in Normandy above the landing sites, the 262 would just be another. Any airfield in France where they were stationed would immediately become the number one target for allied bombers. It is easy to construct fantasy scenarios about what thousands of 262s or others would do but you cant stop thousands of tanks with cannon armed aircraft.
As it was the Luftwaffe didn't feel comfortable engaging an enemy aircraft till July 25 1944, 6 weeks after the invasion, and that was an unarmed PRU Mosquito over German territory where the 262 might not be captured. It ended inclusively with possibly 1 hit by the Me 262 though the bomb bay door that had blown of the Mosquito may just as likely have done so due to manoeuvring. Since he saw parts flying of the Me 262 its pilot claimed a kill.
Lets consider what might have been achieved had Adolph Hitler expectation been carried out:
1 Bomb racks would be fitted to the Me 262. These would latter become useful as drop tank positions greatly increasing the Me 262's range as an escort or reconnaissance aircraft.
That would have avoided Hitler's ire and he would be forced to accept the aircraft was not yet ready.
It could bomb using electronic blind bombing systems. (Fw 190F did use these) but that doesn't attack an invasion fleet.
2 If fitted with a fighter bomber REVI reflector sight it might use the same technique the Me 109 used which is to set a second reticule on the REVI and then at the correct range or altitude pull up until the second reticule crossed the target and release the bomb. The pilot would either set an alarm in the altimeter or use the stedometric range finder in the sight to estimate range.
3 This didn't work well in an Me 262 which tended to get in trouble with Dr Mach forcing the aircraft to slow down to attempt to bomb. The Me 262 bomber would thus need air brakes.
4 Alternatively a toss bombing sight like the TSA 2D might be fitted. This used a precision barometric altimeter or alternatively FuG 101a radio altimeter) in combination with an accelerometer to automatically release the bombs in the pullup at the correct time. All the pilot need to is line up his gun sight and pull up and the bomb sight released at the correct point.
In my view both the TSA 2D and the air brakes would be needed.
So if Hitler orders had of been carried out we might have seen an Me 262 with fittings for a bomb and drop tank.
We might even have seen it with air brakes, as a separate line.
Both would improve it as a fighter and a long range reconnaissance aircraft.
The reality is however the aircraft wouldn't have been ready on June 6 1944 either way and the important TSA 2D bomb sight probably not.
However if the Me 262 had of been in the operational state it was in November 1944 only in May 1944.
1 Reconnaissance Me 262 would have a dramatic effect on the conduct of German campaign even before the Allies landed.
2 Me 262 fighters might have strafed ground targets or assisted Fw 190 and Me 109 in attacking. 100 Me 262 would make little difference.
3 The few JABO Me 262 would have limited capability since without the TSA 2D bomb sight and air brakes they needed to slow down to attack. (TSA assigned to KG51 about Jan 1945)