Sir Sean Connery is probably the most famous Scotsman alive today. He is so much a supporter of Scotland that he has a tattoo on his arm, which reads "Scotland Forever." However, his Connery ancestors are from Ireland.
According to an article in the Scotsman, Sean Connery's great grandfather was James Connery, a tinker from Wexford who moved to Scotland to find a better life. His death certificate showed that he worked in Scotland as a labourer.
Obviously, Sean Connery is still a Scotsman, regardless of where his ancestors came from.
Ironically, the Irish accent he used in the 1987 film The Untouchables playing the part of Chicago cop Jim Malone was voted the worst accent of all time in a poll.