I have heard a lot of people talking on the news about how the laws that are "on the books" are not preventing illegal immigration. The reason for this is, we are not enforcing these laws.
If all the laws "on the books" now are not preventing illegal immigration, why would this new law prevent it?
It would not.
I have never filled out a job application without this section in it:
If hired, can you furnish proof that you are eligible to work in the United States?
Why is this question necessary?
To prevent an employer from breaking the law. If the employers cannot or do not hire them, they will stop coming.