I believe it would work, but at the same time, Amayerasu would be either on ones self or on a comrad/precious cargo. Using particle style would simply damage you even farther. If your asking can you use particle style to clash with Amaterasu head on, then I'd have to say nay to that. It just doesn't seem possible.
So to answer your question, yes it works unless its a clash, but you're screwed either way.
Of course. Dust Release destroys anything it conceals in it's range. So in theory Amaterasu would be erased from existence.
What he said, basically. Within reason, of course.