It should survive. Black Spot is about the most common rose problem.
There's not much you can do once the disease is in place. You can't kill it off. Bear in mind, too, that you can spread the disease via your hands and things like secateurs. The rose will shed its leaves for winter. Gather up all the diseased leaves, destroy them, and always try to keep the surrounding area clear of diseased bits of plant.
Spraying against any fungal disease has to be preventive - which is to say, before the symptoms appear. So if you spray next season, start early.