You don't understand economics if you think that's what would happen. If women actually make 18% less purely because they're women, companies who realize this will be able to hire well by paying women only 15% less. More people will catch on and see they can hire qualified women for only 12% less. And so on until the prevailing price represents something other than "just because they're women".
That's a circular argument. "If wage discrimination existed, then the magic market would have corrected it. Ergo wage discrimination cannot exist." All reports about employers exploiting immigrant labour is false too.
The lower price of (presumably illegal) immigrant labor has a structural difference - the idea is that both worker and employer are taking a risk by doing a transaction off the books.
However, the employer has greater leverage because he can report the illegal to USCIS, whereas the illegal worker presumably has a precarious financial and social situation in the country and has to "take what he can get". Hence, there's a downward pressure on wages.
Whether they are legal or illegal immigrants is irrelevant to the argument presented. The market should identify a "business opportunity" and push salaries upwards to an equilibrium.
There's no pure, efficient, "labor market" but instead lots of small, loosely connected "labor markets" with a variety of inefficiencies - lock-in, friction, imperfect information.
An employer can exploit illegal immigrant labor because it tends to be concentrated in lower-skilled, relatively interchangeable jobs, and because illegal immigrants are in a difficult spot.
