But there was also a CSA regiment with that name:
http://en.wikipedia.org/wiki/1st_Louisiana_Native_Guard_(CSA)
But, as per your own source, this unit was not involved in combat. It was not even allowed to escort POWs. When the Confederate Army needed more white officers, it poached them from the 1st Louisiana Native Guard and that unit was forced to disband. This sequence of events does not support the claim that “thousands of African Americans fought for the South during the Civil War.” If we are to draw any lesson from the 1st Louisiana Native Guard, it might be that, “thousands of American Americans purchased their own weapons and uniforms and offered their services to the South; they were refused, and later disbanded, so most of them put down their arms and the rest joined the Union.”