I remember many years ago visiting a museum in Gettysburg that listed the number of casualties by state and for each side. If I recall correctly (and I am not sure I do, hence asking this question), the number of casualties in the Southern states listed under the Union army was surprising high (maybe 50% of the Confederacy's levels). I am an amateur student of history and particularly the Civil War, and have since never come across anything in my reading that noted a high participation rate of Southerns in the Union Army.
Commonality depends on where you live. For states like South Carolina, Georgia, Mississippi, not really. These were some of the most hardcore secessionist states. Also the geographical locations can really play a major role as well. You don't see many slaves in the hill/mountain country across the south, and a lot of these areas held onto their unionist beliefs, especially after the war started turning sour for the south and the laws made times tougher. These were some of the most hardcore secessionist states. For an area like Northwest Arkansas, yes it was quite common. Arkansas raised 11 Union regiments during the war. Some of them were former Confederates who had deserted the army and returned home to raise a Federal Cavalry Regiment to help protect their families and towns from Confederate guerrillas and bandits. If you're wanting to know about a specific area, I'd ask for that area.