No, the William in the will wasn't a son of John Pace (d. 1726 Chowan Co NC).William is believed to be John Pace's grandson, son of John's son George.This relies on circumstantial evidence plus DNA results of known descendants.
William's son George is believed to be the George Pace who died in Clay Co KY in 1816.Administration on the estate was granted to James Pace. Matthew Pace stood bond.At around the same period, land entries were recorded for a James and Matthew Pace "of Clay Co KY" in Lawrence Co IL.Unfortunately, there's no confirmation that George Pace who died in Clay Co KY was the same person as the George Pace named as a son in William Pace's 1790 will.Unless perhaps you've been able to find evidence for this?
If that link could be substantiated, the line would run back from James like this:
James (George d.1816, William d.1790, George d.1745, John d. 1726, Richardd.1678, George, Richard of Jamestown)
If your wife is in touch with a male Pace relative who would be interested in a Y-DNA test, the question could be answered very easily, since several descendants of William Pace (d. 1790) have been tested.