Politics of it all aside, and purely as a historic journey, yes, due to the highland clearances... an example of ethnic cleansing conducted by the British government over a long period of time. Before the Jacobite rebellions as a way to enforce conformance and hog-tie the Scots and post Jacobite rebellion, bagpipes, tartan, weapons and even speaking Gaelic were banned and punishment ensued. The highlands were emptied of people who were sent to the colonies as indentured slaves, making way for sheep farms. Entire villages were slaughtered by an English general claiming “God will know his own”. At the time poverty was rife. Potatoes made up 98% of the Scot’s diet. 99% of the Irish diet. When the potato famine came thousands died. Crimes like stealing a loaf of bread were punished with either serving in the British army as canon fodder or sent to the colonies as a prisoner (slave labour) for 20 year sentences. The repercussions of the depopulation still resonate today.
Mostly the clearances sent Scots to America, Canada, Australia and New Zealand. Famine and poverty also saw a load of Irish going to America for a better life. Ironically it is why There were so many Scots and Irish in America and why so many sparked and then fuelled the American revolution. Also why Scots help draft and sign the American Declaration of Independence which I understand was influenced by the Scot’s Declaration of Arbroath, 1320, where Scotland asserted it’s independence from England after the English King’s betrayal and greed saw England try to annex Scotland only to be ejected in the Scottish wars of independence with William Wallace (Braveheart) and finally Robert The Bruce.
You might find this Wikipedia entry interesting: https://en.wikipedia.org/wiki/Scottish_Americans
Scottish influence on America is significant. Everything from the congregation model of churches, the Scot’s moral philosophy, the influence of that philosophy and social thinking of Robert Burns on early presidents including Abe Lincoln, through to the Davidson brothers from Harley Davidson lol it’s an interesting connection.