I certainly agree with your thinking here, although I think one unintended consequence is that the illegal alien lobby would use the fact that they paid taxes (under the FairTax provision) to legitimize their call for social services. It would be a politically challenging to deny them services if indeed they pay taxes.
For me, it's a no brainer. I don't care if they pay taxes or not, illegal means illegal, but the jellyfish in Congress would probably be put under more pressure to give in.
The last thing I'd want to see is the illegal lobby working in solidarity with the democrats in DC decrying "Taxation without Representation". We all know the MSM would jump on that in a microsecond.
the truly beautiful part about the FairTax is that below a certain level, there is a rebate...which can force the alien to begin the process of entering the system...It penalizes those who remain here illegally, and rewards those who follow the law. I am convinced that their tax-free earnings presently, in conjunction with "free" social services fuels the problem and impedes those who might otherwise attempt to come legally