Yes. There were quite a few units of Union soldiers from Confederate States. Also several units of Confederate soldiers from Union States. The Union units were primarily colored units. The Confederate Units were primarily from border states such as Maryland and West Virginia.
The US National Park Service has a nice search tool that will allow you to look up nearly any unit and get a brief overview of their history. Just click Union for side and then type the name of any southern state into the "By Name" section.