It appears that there are at least two men named "Richard Davis" in Russell county, Virginia and Fayette county, Kentucky. More research will be needed to separate these two men.
It is somewhat problematic that Elizabeth w/o Richard Davis is always referred to as "Ann", not Elizabeth in the Fayette county records. In Jessamine county, KY and Washington county, Indiana she is referred to as "Elizabeth", not Ann. So that puts this whole family in the "it's possible" but may not be correct category.
Fayette county, Kentucky records seem destined to be destroyed: Levi Todd appointed county clerk and had an office in the new courthouse, but kept the records in a small stone building at his home. This burned on January 31, 1803, destroying most of the records of the Court of Quarter Sessions and the County Court. Later that same year, 1803, the Courthouse itself burned, again destroying most of the records. There are some parts of those burned records which are recognizable and have been searched.
For several years after the probably death of Richard Davis, his wife Elizabeth was taxed on 20 acres in Jessamine county, Kentucky. However, it appears that she moved with her son-in-laws - the Nicholsons - to Washington county, Indiana and died there. A thorough search of the probate records for her clearly name her children.