No man, you're failing to differentiate illegal labor markets from legal labor markets. It is possible to hire illegal immigrants in legal labor markets. ****, I live in Iowa, they're all over here, all the factory towns, and yes, they work hard and do good work, and thus they get jobs in the legal labor market, despite their illegal status.
That is the legal market. And even in the legal labor market illegal immigrants have the unfair advantage of not being able to unionize (I know, seems odd to refer to that as an advantage, but such is the nature of the unskilled labor market, if he's only gonna hire one of us, and you and I have equal skills, he's gonna hire the one that will cost him less, and I am more likely to cost him less if he knows for sure that I am not able to unionize, while you are)
The illegal labor market are jobs that do not abide by the various laws and regulations associated with commerce, most notably on the issue of employer/employee transactions. Protection from dangerous work environments, doing certain jobs in illegal working conditions, work that pays less than the minimum wage, this is the market which illegal immigrants have access to as a product of their illegal status.
And it's not a far jump to the drug market. Drugs are entirely a black market, and thus also will only hire people qualified to work in the black market (and a major qualification is the knowledge that you're not gonna rat them all out, something that can be easily provided by being an illegal immigrant, as to rat them out you'd likewise sacrifice your job, and almost certainly get sent back to Mexico.
That's what I'm talking about.