I don't believe that we truely appreciate the impact that the John Brown Raid had on the psychology of the southern people. The newspapers in 1860 are full of false reports of slave revolts in this city or that, which lead to a certain histeria and laws for the"control" of Free Blacks in the southern states. Hence the rapid growth of local Militia companies.
Even if the South could have armed large units of Blacks, say of regimental size, there would have been a good amount of concern as to the dependabilty of these units in combat. Whether or not they would run when the fighting got critical. For that reason they would have only armed the most dependable Black and have placed them along side white troops usually with their masters.