In that case, the rooster only has one barring gene, so he will give it to some chicks and not others. That would be this situation, with chicks in four categories:
Yes, autosexing requires barring.
It is based on males having two Z chromosomes (so they can have 2 copies of the barring gene) and females have sex chromsomes ZW (so they can only have 1 copy of the barring gene, on their one Z chromsome.)
A chicken with two copies of the barring gene will...