I am also interested in this Dempsey Carroll, but I know very little about him. I am interested in him, because he stated in his application for Revolutionary War pension that he had served in the Rev. from Duplin County, NC. I have formed a hypothesis that he may be a brother to my Alexander Carrell and a son of Dempsey Carrell, Sr. of Duplin County. The part of Duplin where they lived became Sampson County, NC in 1784. If you learn that you are a direct descendant of this Dempsey, I will be glad to send you a couple of documents (a deed and a land grant) that I have on him. I know nothing of his wife or children.
I have noticed an Alexander Carroll later in that area and wondered it he might be Dempsey's son. If so, that would give even more evidence Dempsey might be my Alexander's brother. Since I'm pretty sure the father of this Dempsey is Dempsey, Sr. back in Sampson County, NC, if I could prove he was Alexander's brother, then I would have a father for my Alexander.
Let's stay in touch on this until we prove or disprove the relationship to Dempsey (Demcy/Demy/Demsy) of Duplin/Sampson Co.,NC.