I have 3 or 4 LARGE spools of Coats & Clarks variegated cotton that I found at JoAnn's - used one on a baby quilt and it went fine (pale pastel gradations in "baby" colors).
I've got King Tut, and probably every other brand of variegated thread you can find - I prefer using them because then I don't have to fret about changing thread color when I'm quilting.
I don't know that I'd use variegated thread on SID quilting. It won't really show up.