The percentage of Southerners who owned slaves was never very high. However, I have found quite a few Brogdons/-ens owned slaves but I'm finding it was mostly one or two slaves per family, which was probably more common than the huge plantation work gangs you see in the movies.
I couldn't give you a rundown on how many of them slept with their slaves, but it was more common for slaves to simply take the name of the household to which they pertained. I think this business of slave owners fathering mulatto children has been thrown way out of proportion.
Do consider the effects of Reconstruction and poverty upon the African-American community. This might provide a clue as to where some of these mixtures got started.
I have found it strange that until I got on Genforum, I found many more African-Americans named Brogdon (my spelling) than Caucasians. I never thought of the Brogdons as a group large enough to have brought about such a name spin-off among the other community, but maybe I haven't lived in the right places (Texas, not South Carolina).