Notice that I said "most" arrived in the first half of th 19th Century. As it turns out, however, most persons of Irish descent will discover their earliest Irish ancestors to have arrived in the 18th Century. An even bigger surprise will be that if they were churched at all they were Protestants ~ and I'm not talking about Scots-Irish, but Irish folk themselves.
The fellows coming off the prison barges (and yes, you can find out which ones on the net if you wish) had no papers, no money, little command of English, and probably knew more about fist fighting then any immigrants to America before or since.
There were even Irish people coming to America in the 17th Century, and if truth be told, probably in the 16th Century on Spanish and French ships.
Check your history, google "Irish coffin ships." The germ theory may have been unknown, but contagious diseases were VERY well known. Irish "coffin ships" carrying disease were held in quarantine berths until the disease burned out, and only the healthy (as far as could be determined in the 1840s) were allowed ashore.