@Sophiatude well, depends on how thick the accent is I guess. But at the same time it's pretty easy to distinguish it from other accents because of the use of American English. It's sounds normal enough on TV and in films and stuff because most films are American anyways, but would stick out like a sore thumb if it was heard in Ireland everyday.
I usually only hear American accents in person when I'm at touristy areas or when I'm talking to my friend who moved to America (she's developed an accent).
I suppose an irish accent would sound more off because it's not heard as often abroad and people are awful at impersonating the various irish accents. I mean, I can't do a Scottish accent because it just comes out way more Irish than I usually speak.