Researching Pullens related to my own line, I deduced the following. I will not be doing any more research on this branch of the Pullens, so this is all the info I have. I have no primary evidence for this, only the clues listed. However, my conclusions may point another researcher in the right direction.
Sarah Ann Pullen/Pullem/Pulliam married Willis T. Brooks on April 25, 1840, in Tallapoosa County, AL. This info is from the Ancestry AL Marriage Index. Willis T. and Sarah and their children show in the Arkansas censuses from 1850 until at least 1880.
I kept trying to connect Sarah to my Pullen family from Tallapoosa County, Abraham/Abrahm & Liddie Pullen. She was born in GA in the right time frame to be in their family, and Abrahm and Liddie always show as coming from GA.
However, in addition to the Abrahm Pullen family, there was another Pullen family in Tallapoosa: William N. or H. Pullen and his wife Nancy (maybe Abrahm's brother?). In 1850 William is in Arkansas, born NC, Nancy is born SC. Sarah always shows as born in GA. However, 1880 shows that Sarah was born in GA, her father was from NC, and her mother was from GA. The fact that both Sarah's parents were not from GA is one clue that Abrahm and Liddie were not her parents. The similarities between William & Nancy's birthplaces and the birthplaces listed for Sarah's parents in 1880 is another.
In 1840 William H. Pullam is in Tallapoosa County with a daughter in the right age range of 15 - 20; Sarah would have been 17. Nearby are several Brooks families with boys in the right age ranges of 15 - 20 or 20 - 30for Willis, who would have been 20ish. A. Pullen is not around as far as I have found.
So it seems to me that the parents of Sarah Ann Pullen/Pulliam are William H. and Nancy and not Abrahm and Liddie, 'though they may be related.