No, they will be mixed barred chicks...coming out all barred, both sexes, with likely red bleed through as the rooster has.
To create black star chicks, you need to have a pure red based roo with no barring and a barred female. The female will pass barring onto only the male chicks (barring is linked to sex on the same allele) leaving the female chicks unbarred and carrying the red base from the father to bleed through the black coloring from the mother.
You will have fine barnyard mixes from your pairing, but all barred, both sexes.
...and Black Star is not a breed but a particular mix, hybrid, using genetic facts that produces sex identifiable chicks as the boys are barred (white head dot) and the girls no head dot...when applied to a black base that the Barred Rock gives...this makes for easy identification of the chicks.
Sex linking can occur anytime the hen is barred and the rooster is unbarred, but unless the background color is dark enough, the white head dots are not easy to see on the male chicks for sex identification (the purpose of the hybrid).