No, its not nearly abrasive enough. You're probably not going to be able to REMOVE the swirl marks with anything by hand. You can use a product like a glaze to fill them in, but within a wash or two they'll be back. They're scratches in the paint, the only way to remove them is to remove paint around them to level the surface off.
In order to remove them you're going to need an abrasive, like a Swirl Mark Remover or something even stronger possibly, an orbital polisher with a cutting pad or a rotary polisher possibly. Difficult to do by hand, not impossible, but difficult.
Think about it this way, there's reasons people pay professional detailers. If the "3 step system" just wiped stuff like that out...