I’m a bit skeptical about that. The military was ordered to integrate in 1948, but the Army dragged its feet until the Korean War broke out. There, the Army was so desperate for troops, any troops, that trying to maintain colored and white unit differentiation proved too problematic. If integration was successful six years later, under far more trying and chaotic circumstances, why couldn’t it have been possible in 1944?
If the war had gone into 1946 I suspect that you’d have seen a much larger contribution along the lines of French African Troops in WW1.