It definitely affects these figures, because they are filtered out of the income statistics. Just one of the many ways figures are skewed.
Another is the low-paid jobs done without proper employee registration by immigrants.
Because construction, lawn care, and sweatshop jobs by immigrants is all registered in the US.
The “lack” of social system in the US that hides in the EU millions upon millions of people who don’t work for various reasons (ranging from not wanting to down to not being able to or not being employable) is definitely something that makes EU look better than it should. In many cases, they don’t even appear in the officially unemployed statistics, because they are so called social cases. At the same time, many of them also work “unofficially”, so they often end up earning more than honest people, while working much less.