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Great discussion. I think, too, that we need to make a distinction between drafted and pressed into service. My research on the Civil War on the lower Mississippi (Louisiana in particular) indicates a great deal of pushing liberated slaves into the ranks, willingly, unwillingly, or perhaps unwittingly. Research using original muster rolls and even the WPA slave narratives indicates the when officers had a need to fill the ranks (desertion rates were very high) they went shopping at local plantations. Need a farrier? There is one over on the Labadie place!
To follow up on William Kurtz's reference to civil war data: I've found uadata.org to be a more reliable source than civilwardata.com. 16% of the black troops in the uadata "extended" sample are listed as drafted, whilst the majority (54%) in that sample are listed as substitutes. If we combine the "extended" and "original" samples then only 7% of all black troops were drafted and 24% were substitutes, the majority being volunteers.