They have to be barred, else they are not black sex links.
Black sex links are mixed breed chickens that are specifically bred with the intent of being able to tell males from females at hatch by the color of their down. There are several ways to do this, but in black sex links, it is the sex linked barring gene that is being used. They are bred such that all male chicks inherit barring, and all females don't. This means all male chicks have a white head spot in their down, while females lack this, and that's how the genders are told apart at hatch.
So a black sex link male MUST be barred. If a male chicken is not barred, it cannot be a black sex link.