As a disclamer, I would like to point out that there is not a spesific reason that caused the Great Depression. It was a result of various factors coming into play in a unique manner. There is no consensus regarding what was the '' main driving force '' among economists.

After making that clear, I still think we can say that the casulties of the great war was not relevent to the great depression and here is why :

U.S casulties in the world war 1 totalled to 116000

Us Population during that time was 103 million.

Labor force participation rate among men was around %85

At the beggining of U.S entry to war, there were 1.9 million unemployed. 0.5 million to 1 million during the war and 1.6 million at the end of the war

Not the mention that there was not a shortage of labor by any means, losing 100.000 people from the labor force of 50 million is irrelevant as far as economics goes.

I dont know how not to sound cold while saying this, but the death of 100,000 from a population of 100 million is not enough to really effect things in major scale, especially not in a way to result or at least contribute to something as big as the great depression.

I hope this is satisfactory for you because frankly, I felt the answer was a bit simple. In my defence, although the effects of great war on the depression is thouroughly researched and debated; the casulties as a factor is not something you encounter very much. And I believe the reason behind that is the irrelevence i tried to show in my answer

Cheers.