I doubt that very much. I know illegals who are making as much as US citizens, and in are valued by their employers because they are hard workers.
Making as much as someone on the books costs a fraction of what it costs to pay someone under the table. I have no doubt that the employers love to pay just wages and let society pick up the balance.
They are just as willing to pay Americans under the table as illegals.
And they do it all the time. It's nothing new or unique.