Roz, do you have any sources for the information below? I'd be interested to learn if so.
While I was taught at school that Northern Irish English (itself very much closer to English as it was spoken in England during the reign of Elizabeth I) was an influence on American English, this was qualified and limited - being mainly the case in the pre-famine waves of migration.
The cultural and linguistic impacts of the Northern Irish (including bluegrass music) were thus more prevalent in the Appalachians/Virginia and have survived there as a lasting influence.
During the time of the Great Famine, the rate of emigration from what would eventually become Northern Ireland was much lower both in percentage and absolute terms than from the rest of the island - Belfast actually grew in size quite substantially in the period 1841-1851, as reported on wikipedia - so any cultural impact from the specific Six Counties would have been diluted on the far side of the Atlantic.
Going slightly back to the overall theme of pedantry in this thread - "being forced into famine by the English landlords" does only tell part of the story - potato blight played a part, as did the lack of conscience among the Anglo-Irish aristocracy. I would quote Alan Partridge on this, but I don't think you'd appreciate it, somehow.