Years ago in California, we had a case like this. A son of a landscaper (who had worked around the property with his father and thus was known to the homeowners) accompanied by a friend came back to the house and asked to make a phone call. The men attacked the couple, raped and tortured them, made them crawl around the house naked, and finally killed them - or at any rate, they thought they had, but the woman survived and was able to identify one of them. They were native born Americans, one being the son of the hard working black man who was the landscaper hired by the couple. The son had apparently gotten into "black power" stuff and thought this was the way to express it. IIRC, they did not get the death penalty because in California in those days, they couldn't (especially in a black on white crime).
My point is that his immigration status is not the important thing, but what is important is that he should have gotten the death penalty. The problem is that countries whose citizens commit capital crimes here protest vigorously against the death penalty, and are extremly uncooperative about extraditing them if they manage to make it back to their countries of origin. I think we should put lots of pressure on these countries, and if their citizens commit crimes here - regardless of their immigration status - they should be up for the death penalty just like anybody else. (That said, does NY have the death penalty?)
I don't believe that NY has the death penalty. My greater point is this.....his immigration status does count. If we had been vigilant about booting illegals, he wouldn't have been here to do this! The longest walk starts with the first step.