You shouldn't be getting your history from "Gangs of New York." While there were recruiters in New York appealing to immigrants, conscripts in general comprised only 6% of the US army, including substitutes paid by draftees. Confederate conscription rates are hard to judge because the records are spotty, but the best estimates are that they were about double that. But the number is misleading because, while the US army released enlistees whose contracted term was up, the confederate government passed laws extending enlistments for the duration, essentially drafting their own soldiers.
Actually, many of my history classes talked about the regiments that were made up of Irish immigrants.