Productivity Measures

I've heard the argument that nations like France have an overstated level of productivity per hour worked because their economy has eliminated jobs for less productive workers without finding them more productive jobs (high unemployment for the young and under skilled). But in arguing that are we missing something about US productivity? The United States, as it has been repeatedly pointed out recently, has 11 million migrants who are staying in the country illegally. How are or are not their hours counted towards the total numbers of hours worked in America each year? Could US productivity numbers be inflated by undocumented unskilled work?