There's another side to the story of the Irish in the Civil War and immigration in general in Kevin Baker's novel "Paradise Alley". Some of the New York Irish rioted over the draft, which could be avoided by the rich for $300. The story is definitely not for the faint of heart: Both the descriptions of the famine and the riot are pretty gruesome.
The book also points out something that proponents of immigration choose to ignore: Every wave of immigrants -- including my own family -- pushed both Native and African Americans down even further. It wasn't until the Depression brought a halt to immigration, followed by the industrial ramp up during World War II, that both the labor movement and African Americans began to get a foothold.