As retired military and working for a service headquarters, I can tell you that Dixie hit the nail on the head. They would be a security concern if anyone accepted this suggestion (which by the way, is all it is at present). I can remember an earlier post whereby I talked about the relationship with the country of the Philippines. They were one of very few exceptions where the Department of Defense through the Department of State allowed individuals to sign up and serve in exchange for citizenship. But that situation was a little different. We had paper trails on the individuals through the host country, etc. With illegals, you wouldn't necessarily get a paper trail. Just look at the illegals now with convictions, on the run, or never showing up for court?
I would say that someone would have to be "out to lunch" if this idea ever got farther than a thought...