As far as I am aware the Scots have both a Celtic (Gaelic) tradition and an 'Anglo-Saxon' (for want of a better term!) tradition - after all the great ballads from the North East aren't in Gaelic, are they?
I think that 'Celtic' - at least as understood by the media - is mainly a lot of silly Nineteenth Century romanticism (with some fairly crude nationalistic undertones). As far as those same media are concerned 'Celtic' consists of, mainly, Irish Uillean pipes (usually standing in for Highland bagpipes) and Enya singing down a well! All very tiresome - and, as far as I, an Englishman, am concerned a complete misrepresentation of the cultures of our great neighbours the Scots, Welsh and Irish, for whom I have the greatest respect (they, of course, are free to disagree with me).