Would the allies have lost even if Operation Overlord would have been a disastrous failure?
I don't think so. The defeat of the German forces had been sealed long before that. No doubt of course that it would have prolonged the war, but it would certainly not have caused a German "victory" (what a disastrous defeat such a "victory would have been!!!). With all the speculation about German "secret weapons" it is often overlooked that the allies where already on the overtaking lane in many fields of military technology. The development of the nuclear bomb is just the most prominent example, but jet fighter airplanes were developed by the allies as well though they did not feature prominently in WW2 anymore (the P-80 Shooting star which was superior to the German Me-262 in about every respect had its first flight in November 1944). Moreover D-Day or no D-Day, Germany was running out of almost everything in 1944. Most of the jet planes build in Germany never ever took of before they were destroyed by the bombs (which could be delivered to about any place in Germany due to the total air superiority of the allies) simply because there was no fuel for them anymore. While the bombing of Germany did not "brake" the morale of the German population as to make them rise up against Hitler and the nazis, the mood among the German population at the time of the invasion was that of resigned despair (few being as naive as to believe in the "Endsieg" (final victory) anymore, but hardly one ready to offer any resistance to the regime).
June 6th 1944 was the day which heralded the end of the war in Europe, but the outcome of the war had been determined long before that.