No one could sneak in from Ellis Island. They were sent back if they had any illness, any descrepancy of their documents, any thing at all that would cast a doubt on their being a productive person if allowed to enter would get them sent back. The whole reason of Ellis Island was to sift through the undersirables and eliminate them. You couldn't "sneak" off of Ellis Island unless maybe you could transform yourseld into a boat!
Most of the Irish came here BEFORE Ellis Island was established.The waves of Irish immigration started in the early 1800s, building to a peak around the 1850s. Ellis Island didn't come to be until almost 1900.