Again, a case can be made that this difference corresponds to that between a pantheistic (there is an inherent order to the Cosmos corresponding to the order theists ascribe to the will of God) and an atheistic viewpoint.
Well, all right. I could probably make the case that singular events can occur even within orderly systems, i.e. "accidental" doesn't imply "chaotic," but it's really a tanget. So if you wish to call me on that point, I can change the phrasing to "an inevitable product of physics and chemistry," and the remainder of the sequence can still stand. Without God, it doesn't matter if we perceive the universe as orderly or chaotic; either way, it remains without purpose, a natural sequence of events that just happen.
Again, a case can be made that this difference corresponds to that between a pantheistic (there is an inherent order to the Cosmos corresponding to the order theists ascribe to the will of God) and an atheistic viewpoint.
Well, perhaps. In this case I would raise the point that our universe is what it is, and the fact that you see order in it may say something about the universe... or it may merely say something about you. Remember, there is no God in this little thought-experiment.
Or, to put it a different way... orderly compared to what?