Yes, or at least, they can.Does the world exist for the NPC's?
I don't think that is uncommon actually. I think many DMs have written worlds without having players -- either as thought experiments, tinkering, world building for fun or the basis of writing stories. Probably most of what DMs create is never interacted with by PCs. From my observation few players care about the details of world building. These are the same players when they get to long dialogs in CRPGs just skip write through them.
I suspect that may be overstating it, but have never seen any hard data. But, assuming that's the case, wouldn't they generally answer 'yes' to your question, because it's a creative outlet, rather than because "The world exists for the NPCs?"Meh. Almost every fan of anything in the sci-fi/fantasy genres is a frustrated novelist.
It's a common confusion, but for the purpose of this topic I think we have to be very clear - PCs don't play in the world, players do. I think it's a much less interesting question as to whether the world exists for the players. The game and thus the world exists for the game's participants.
With respect, I don't think anyone is confused here, any more than they are confused when they talk about killing players instead of killing PCs.It's a common confusion, but for the purpose of this topic I think we have to be very clear - PCs don't play in the world, players do.
Yes and no. Yes, I have things that happen off-screen often without the input of PCs. Either because the group didn't follow that path, it wasn't relative to the PCs at the moment or because it's happening between campaigns.