I don't know about singing with Scottish accents, but some of those bands listed do have a certain Scottish element to their music, with elements of Scottish folk in it. Mind you, Irish and Scottish folk music were big influences on American music, which in turn has influenced Scottish music... Bands like Big Country and Deacon Blue have a Scottish "sound" to them (in my opinion).I've vaguely heard of them but I had no idea they were popular in the USA. Then again they're not really my type of music. Apart from Annie Lennox, Sweet Dreams and all that. None of them sing in a Scottish accent though as far as I know, their music is indistinguishable from American music to my ears, which is what I mean by not really 'Scottish'.
And then you get a few bands like Runrig and Mánran, or singers like Julie Fowlis, who sing in Gaelic (some of the time) and who are very Scottish! (although not quite so mass appeal, but they appeal to me!).