Yet they had to draft immigrants as soon as they came off the boat. Somehow, that doesn’t suggest they weren’t starving for manpower.
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.
And the Lost Cause myths just keep coming.