Over what period does this law apply? If you are a multinational and you bring workers over for a two-week training course, do you have to give them a raise for those two weeks?
It is probably unusual for companies to bring people getting paid less than U.S. minimum wage to the U.S. for a two-week training course. Why would you spend so much money (travel? hotel? they're staying in your basement?) on workers you're paying less than minimum wage?
We frequently sent people to India and China to give training, especially when building out a new office or department. Occasionally, we would fly someone here (the US). Not so much for training but more to meet the the team.
With the caveat that I am not a lawyer or accountant, I would expect (but since when are laws reasonable) that if the person flown to the US doing so for a short time period and moving to the US, their pay would not need to change. But I could be very very wrong.
http://flsaovertimelaw.com/tag/undocumented-immigrants/
The decision went to the text of the Federal Labor Standards Act and decided that it had a very broad definition of employee. I wouldn't expect narrower decisions for companies flying people around for training.
For $200 a week, and given the narrow availability of visiting worker visas, it doesn't seem like it will come up very often.
I'm genuinely curious. California minimum wage is $9/hour, or $18K for 50 forty-hour weeks.