No, not quite, OP's idea is based on the premise that gay megacompanies hire illegal labor because it's cheap. The idea being that the pay floor would be raised such that there's no longer an advantage to hiring illegal labor. Why take the risk hiring illegals that could be ICE'd on any given day that absolutely cannot be discovered through the likes of OSHA claims and such, especially when that all results in the company losing its labor force on top of potentially being smacked with fines? It becomes more trouble than it's worth.
The problem with OP's idea is that a lot of that pay is probably under the table, chalked up as rounding errors on the books so the IRS doesn't come knocking or something other. In any case, if that pay isn't being documented to begin with then mandating it be raised doesn't do anything since it wouldn't be reported to begin with. I could be wrong, but I'm under the assumption that a lot of illegal labor is paid under the table.