Now, think real hard on this question ~ if, in the 20th century, with high levels of detection available, ships can actually enter and land passengers in the United States UNDETECTED, just how difficult do you think it was for them to do so in colonial times, or even up to the time of the Civil War?
BTW, that site estimates the illegal alien population at about 5 million.
I know a bit about the Irish diaspora. Your scenario of coast hopping Irish cruise ships does not match what I have read, not at all.