Bullsh!t. If the government instituted a draft tomorrow to fight a war of liberation for Mexico, and Mexican immigrants in the U.S. were exempt from the draft, I can assure you that nobody on FreeRepublic with an IQ over 50 would report to their local recruiter.
Their lives were much better than that of the slaves.
That's not as clear as you might think. A family of Irish immigrants living in Pennsylvania lived a pretty miserable life, and they were exploited in a manner not much different than slaves were. Sure, they were "free" in a theoretical sense, but when you are lving in a company town and working in a coal mine at the age of nine for a meager wage that must be spent at a company store, you are not much more than a slave and don't have many options.
The one thing that eventually made life better for the Irish immigrants (as opposed to slaves in the South) was the influence of a powerful, paternalistic Catholic Church that took upon itself to serve as an advocate for these immigrants (I'll bet most people weren't aware, for example, that the Knights of Columbus were originally created to serve as a life insurance company for Catholic working men). In general, the most influential leaders in the history of the Catholic Church in the United States were from that era.