The best example of blacks in battle during WW2 are the Tuskeegee airman, who performed extremely well. It sounds like you were asking about infantry, but being a pilot, especially a combat pilot, is much more difficult than being an infantryman.

I doubt there is a strong relationship around race or ethnicity and combat effectivness because there are too many other factors.

For example, if you were to take the kenyan jungle militia and put them against a "well trained" unit of American soldiers, and leveled the odds by giving them the same equipment and support, I would put my money on the jungle men. Why? The american soldiers spent the last month sitting through powerpoints on rape and suicide prevention while the kenyans were defending their village from a rival warlord