Some work. Many don't. And the ones who do work aren't generally doing anything inherently better and are doing the work that natives were doing long before their arrival and still are doing!
Immigrant worship has played out!
Having known many people who became illegal immigrants, I have to agree with this.
Illegal immigrants are not an homogeneous monolith, as some people want you to think.
A few groups I've noticed are:
The ones who can afford to go as tourists but end up staying as aliens. They are usually middle class, with good manners and an average education (perhaps below average by US standards).
The ones who will risk their lives in order to enter illegaly. They are usually less educated than the first group. They can pay up to 15K-20K to coyotes so they take him to the US. That amount of money would allow them to start a small business where they come from, yet they choose to leave their country.
People who go to a foreing country only because they have relatives there. This is a really heterogeneous group. Hard to make a generalization about it.
Hardworking, frugal people who pursue high paid jobs in order to save as much money as possible and send it back to their country so they can come back one day and invest it. A small group in my opinion.
People who come from colapsed societies like Venezuela, or Siria. Again, hard to make a generalization about them, except that they had good reasons to run away from the country.
All in all, those gruops are not mutually exclusive. I guess some of them overlap oftenly.
PD: I'm talking only about latinos.