Not really. When most of the Irish came, (1830s to 1870s) there was no such thing as an Ellis Island facility and immigration was not really controlled in any way. Ships docked at there destinations be it New York, Boston, Philadelphia, Baltimore or where ever, the the passengers basically got off and went where they could. There were customs offices that looked a cargo for duties, but no INS service that checked passengers. It was pretty much an "open borders" policy.
You have it right. Most of the Irish did NOT come through Ellis Island. And (in the case of my forebears -- 1845, arr. Philadelphia) they were granted citizenship right on the ship before landing by "declaring" for their new country.