No, and there is no evidence whatever that William's wife was Snodgrass.I gave her that label myself, about 30 years ago and early in my work, by mistake.
Stephen is known to have married, 2nd, to Mary Batten, widow of Joseph Batten of Fayette Co, PA.(Batten was the brother of Henry Batten, who lived on the site of Rivesville, WV.)This is attested in an 1803 complaint by Henry Batten to the Monongalia overseers of the poor, stating that Fluharty had married the widow Batten and was neglectful of her children.NB the 1810 marriage bond of Jacob Fulkerson and Catherine Batten, which includes a consent from Stephen and Mary Fluharty.The Stephen who signed this is the same one who was pensioned in Harrison Co in 1818, as his signature shows. All of his signatures in Monongalia records are identical.
In 1835 a Mary Fleharty, of Washington co, OH, sold her interest in the lands of Charles Snodgrass.There are several early references to Stephen Fluharty in connection with Charles Snodgrass, though none which are explanatory.It appears to me that Mary Snodgrass (c1775?-aft 1842) married, 1st, Joseph Batten, and 2nd Stephen Fluharty.A deed of 1842 in Marion Co calls her "now Mary Thorn" and implies that she was still living at the time though it does not say where.All the other heirs of Charles Snodgrass sold their interest in 1811 -- 9 in all.This Mary conveyed a 1/10 share of the property in 1835 but without stating that she was a daughter of Charles, who had been dead since 1808.
It seems probable that she and Stephen went to OH sometime around 1811 or 1812, when other members of the Charles Snodgrass family migrated there, and that they later separated by mutual consent.In 1820 Fluharty was living alone.Although the 1790 census suggests that he might have had issue by his first marriage, there is no contemporary evidence of it.The only Fluharty of that period who can be placed as to parents by contemporary evidence is John, who brought a suit in Monongalia Co, 1803, stating himself to be the son of Noah and Nancy (Reeves) Fluharty and referring, without naming them, to his "sisters & brothers."
I have never found any documentation as to the identity of Mary (c1790-c1840s), first wife of William Fluharty of Monongalia and Wetzel Co, WV.