For reference, the AR-Gov race in 2018 was 65-32 for Hutchinson. Phillips County was the most Dem county in the state, going 54-44 for the Dem. Next up was Lee, going 53-45 for the Dem. Those are the most likely, and with Lee’s small population of only 10,000 or so, if Harrington Jr. actively campaigned there he might squeak by with a majority.
I don't see why anyone in those counties would turn out if there isn't even a de facto Democrat like Dan Whitfield on the ballot.
The number of people who don’t turn out to vote in a presidential year because there’s no Democrat candidate in one single down-ballot race which would have been non-competitive even if a Democrat had been on the ballot is closer than zero than Harrington's chance of winning a county or two.