The only Drennen-Thompson connection I am aware of is John Drennen b. 5 Feb 1801 in Elizabeth PA, d. 27 Sep 1855 in Indianapolis, Indiana while traveling from Van Buren, Arkansa back to PA to visit family. He married Emily R. Deaderick b. 15 Jul 1799 in Frederick, VA, d. 20 Aug 1844 in Van Buren, Arkansas. Emily's sister Laurette, married David Aiken Thompson b. Apr 1799 in Delaware, d. 12 Sep 1839 in Arkansas.
John and his brother-in-law David Thompson were in the merchantile business in Nashville, TN. They went on to co-found the town of Van Buren, Arkansas.