No, any leaves that are already infected will yellow, die and fall off. It's not mandatory but picking off any of the already spotted leaves will make your roses look neater. Don't worry if they look bare, the leaves will grow back. And be aware that there may be more leaves that look clean now but that are already infected that will continue to spot for a bit. The spray will only keep leaves that are not already infected from being infected. You will also have to spray on a regular basis to keep them from getting infected later.

Black spot spores are everywhere all of the time and only need the right conditions to grow. High humidities and temperatures between about 68 and 78 degrees seem to do it here. And the name "Black Spot" covers a variety of types of fungal diseases not just one. So the variety of spores I have may be different than the ones you have. But most good fungicides will kill most varieties.

There are reports that Bayer's tebuconazole spray (Bayer Advanced Disease Control)will actually heal blackspot leaves. I've certainly seen something similar on mine. I've seen blackspot-infected leaves with spots segregated, bordered off, and then the rest of the leaf lives on.

So, I would recommend spraying, be patient, and see what happens.