Actually we wouldn't need to round up any illegal aliens. Instead, we need to:
1) Cut illegal aliens off from all taxpayer funded services.
2) Crack down hard on employers who hire illegal aliens.
3) Kick able-bodied Americans off of welfare.
4) If necessary, increase the number of LEGAL immigrants that we let into the United States.
By doing these things, illegal aliens would have no access to any jobs or any taxpayer funded freebies. Most illegal aliens would likely make the decision to voluntarily return to their home countries.
I agree with your theoretical method of curing the illegal problem - unfortunatley, as a political issue, your ideas are no more PC than the ones I mentioned.