hanes teulu,
No, that road goes from York to Scotland but if Scottish drovers used it, they would have branched off somewhere north of Consett, perhaps towards Shotley Bridge.
The map was revised in 1895 and shows the whole of Sherburn Terrace but, when the Target/Grey Horse was built, there were large gaps in Sherburn Terrace. If you look carefully, the pub was located on the road just below the second r in Carr Ho(use). Carr House being the extreme edge of Consett (or Conside and Knitsley as it was then known).
This map no longer shows the footpath/drover's trail that existed at the time and is now all built over. It is so frustrating as I live only about 2 miles away from the site of the pub and I can find virtually nothing on it's history!