Of course it is.
Interesting footnote: the colored troops in the South were integrated. I always thought that was ironic....
And mythological. When the rebel government got around to authorizing black combat troops they mandated separate units for them Link. Prior to that any blacks attached to a rebel unit were there unofficially as servants, laborers, teamsters, cooks, musicians, and the like. Kind of hard to have someone waiting on you if they weren't right there with you.
"Over 3,000 Negroes must be included in this number [Confederate troops]. These were clad in all kinds of uniforms, not only in cast-off or captured United States uniforms, but in coats with Southern buttons, State buttons, etc. These were shabby, but not shabbier or seedier than those worn by white men in the rebel ranks. Most of the Negroes had arms, rifles, muskets, sabers, bowie-knives, dirks, etc.....and were manifestly an integral portion of the Southern Confederate Army."
Frederick Douglas reported,
"There are at the present moment many Colored men in the Confederate Army doing duty not only as cooks, servants and laborers, but real soldiers, having musket on their shoulders, and bullets in their pockets, ready to shoot down any loyal troops and do all that soldiers may do to destroy the Federal government and build up that of the rebels."