This question relies heavily on assumptions that are largely incorrect. For one the Germans were losing horribly by the time the allies invaded Normandy in 1944 and their war production was about as high as it had ever been. The largest problem Germans faced at that time wasn't so much a shortage of labor as it was a shortage of resources. Jews were used alongside other foreign nationals for forced and slave labor - even if the 6 million or so Jews that were exterminated had been used for labor it wouldn't have changed the reality of extreme shortages of strategic materials.

By summer 1944 the Germans had lost spectacularly large amounts of men and material on the Eastern Front. Their offensive had stalled prematurely at the gates of Moscow in the Winter of 1941 in the ill fated Operation Typhoon, and subsequent massive Soviet counter offensive that put the Germans on the retreat for a short time. Their second attempt at finishing off the Soviet Union in Operation Blue by Army Group south for the oilfields in the Caucuses and to cut the Volga at Stalingrad was not only a failure, but resulted in the encirclement, destruction, and capture of the entire German 6th army - hundreds of thousands of men were wounded, dead, or captured in the aftermath of the disaster. The entire balance of power then shifted to the Soviet Union after the fall of "fortress Stalingrad" - then later that same year in 1943 the Germans at the behest of Hitler attempted to reverse their fortunes against by attacking a salient in their line formed by a Soviet offensive following the fall of Stalingrad. The Soviets not only knew of their oncoming offensive, but even the exact date of the operations execution (Operation Citadel to be precise). The attack, while delayed for the arrival of newer Tiger and Panther tanks, was a failure - it saw some of the largest and most brutal battles in Human history, with the single largest tank engagement yet seen. After that point any ability the Germans had evaporated under the weight of massive casualties and losses of valuable german tanks and aircraft. And in the Summer of 1944 Operation Bagration completely destroyed army group Center and routed the Germans from the remainder of Soviet land - the soviets would continue their drive through the rest of that year to 'liberate' Poland. By the time of Operation Overlord and invasion of Normandy, the Nazi's were not about to win - they were on the verge of total collapse.

Aside from being on the edge of complete military defeat on both fronts (although they were not finished off yet, and fought a bloody, and prolonged retreat back into German territory). Their war production situation, while dire, was not so much a result of a shortage of labor (which there was an acute one) it was due to a lack of supplies with which to make war. German oil supplies by 1944 were close to the breaking point and synthetic coal production plants were heavily damaged by this time. They didn't have enough steel, coal, minerals, or other materials to sustain themselves. Even in the event that the Jews had either not been discriminated against - which is a complete lunacy and fantasy land seeing as large parts of Nazi ideology are based on anti-Semitism making it inseparable from it - it wouldn't have done much to change the dire straights in which the Germans had found themselves by 1944 in their "total war".

If anything, had the Germans not went on a campaign of extermination against the Jews it would have harmed them. The Germans brought in billions in revenue from seizing not only the immediate possessions of Jews in camps, but also their property and assets. Billions in revenue would have been lost had they not taken everything from Jews in Europe and would have deprived them of funding. almost half of what was paying for German expenses alongside heavy taxation was expropriated from occupied territories and conquered peoples - primarily among them Jews.