My father's parents were Jews from Poland (then part of the Russian empire). It is not likely that any Scots or Irish got into that bloodline, tho you never can tell. (There is a family of Hamiltons among the Russian nobility -- see Child's documentation on "Mary Hamilton".) My mother's mother's maiden name was Magdalena Carolina Wilhelmina Augusta Oppermann, so she was presumably part of the large 19th-century German settlement in the middle west. My mother's father's name was Hughes, and he was a Methodist, so one presumes he was of Welsh descent -- but some branches of his ancestry had been in the U.S. from before the Revolution, so who can say what got mixed into that? Scots or Irish would be a pretty good bet.

Probably there are some Americans who could reasonably be guessed to have no ancesters from Scotland or Ireland. Say, the ones that came straight from the mountains of Vietnam. Their grandchildren, however, are likely to be open to suspicion.