Yes - and I actually know quite a few.  And many of them are trying to make things right.

Much of the problem with illegal Polish and Irish immigration is the prejudicial system.  In assisting a Polish priest with some immigration problems, I actually had a US Congressman - Democrat, btw - tell me that it would be easier to get a "deranged Imam" into the country that a Polish Catholic priest.  That was about 3 years ago.  Luckily, we were able to get him in.....

BTW - there are estimated to be around 50K Irish and 70K Polish undocumented in the US.  And according to PEW - over 11 Million in 2014.