I think I understand the question. The disagreement seems to be what "undocumented worker" here means.
If you think it means the worker is on the books, but is not a citizen, then you get to your question. It should be roughly the same.
If you think it means that the worker was off the books, regardless of citizenship, then you arrive at the other.
My consideration is if I am a cleaner and get my child to help out on a few jobs, my child will not be a documented worker and it will be a transparent boost to my productivity. Indeed, many subcontractors and migrant workers will use family as a cheap way to boost productivity so that they can take more jobs.
I grant that construction may land on the other interpretation. There are usually more rules for that kind of work. (Though, in rural areas? Not sure.)