Greg-

No, nothing mythical about the Scots-Irish, and very little Gaelic about them either. They were not a race, either (whatever that means), but a almalgation of lowland Scots, border dwellers, northern English (with midlanders and southern English mixed in as well, though Ulster generally was not a destination of choice for southrons).   No need to rehash too much of their history in the British Isles and North America, but there is plenty of scholarship (not just magazine articles and websites) to keep any interested reader busy for some time.

A few points should be made. Briefly, Scots-Irish and other northern British populations were strongly represented in the populations that settled in the North American backcountry in seventeenth, eighteenth and nineteenth century. Many settled in Appalachia, others further north, and others went west to Missouri, Arkansas, Texas and beyond. Given that the core of the Scots-Irish population was Anglo-Scot, the lack of Gaelic songs and place names in Appalachia should not be surprising. As far as their influence upon the music and folkways of the upper South and Southwest, it's less important to count raw numbers than to consider where the Scots-Irish went and what they did when they got there. And for what it's worth, contemporary observers, historians, and geographers have long noted the presence of this population in the backcountry (including but certainly not limited to Appalachia)and their influence upon both regional and national culture in the United States.