Not to my knowledge. I've been studying the Late Unpleasantness for a good 30 years - with a particular interest in uniforms - and I've never heard of a Confederate Highland regiment.

There were certainly Scots and those of Scottish heritage in the Confederate service, but not organized as a "Scottish" regiment in the sense of wearing tartan and having pipes. (I've seen photographs of Confederate soldiers wearing checked trousers - but not tartan)