An interesting debate to be sure, but to be clear Limorrj's figure is a Union soldier, despite the South Carolina Volunteer name, they were a northern army unit formed from escaped slaves from South Carolina. I'm sure there were plenty of African-Americans that (maybe relucutantly) fought for the south, but not even close to the numbers that fought for the Union. As far as integration goes, the south was probably hesitant to arm a whole regiment/company? of armed slaves and send them on their way. They were probably integrated into regular units to keep them under watchful eye. Just my thoughts.
Yes, as a Union soldier that fits in, and there were a number of Union 'colored' regiments filled with volunteers. The most famous, of course, was the 54th Mass. And yes, they were paid less than white soldiers, officered by only whites, and generally not treated nearly as well. Freed slaves were often enlisted, sometimes as soldiers, sometimes simply as teamsters or camp cooks, or work crews. Almost all slaves in the South who were impressed into service were given tasks that didn't involve them having access to guns.
As you mentioned, there was extensive discrimination, and segregation, of blacks in the American forces until after WWII. Still, there were some strong black units, such as the 9th and 10th Cav (Buffalo Soldiers) who fought against the Apaches, and the Spanish in 1898, as well as Black units from NY who served in WW1.
