Absentee ballots

Do American Boards of Elections always count absentee ballots? Or are there circumstances where they would decide they did not need to count the absentee ballots that year?

Yes, they always get counted. Answer Person could find no evidence of a state or county that doesn’t. Sort of the same reason why they don’t just stop counting votes when someone gets to a total of 51% of the registered voters and thus becomes mathematically impossible to beat (unless, of course, you’re talking about the US Electoral College system for presidential elections …).