In general, I think that if you avoid the actual adventure you'll be fine. Guide to Korvosa is a great sourcebook, in my opinion and if I were to run Curse of the Crimson Throne (predominantly set there) I'd encourage all of my players to read it.
I think the only time you'll really get in trouble with the Campaign Setting line is if your DM runs some homebrew adventures there built off the various plot hooks. As a general rule though, even if you're reading the sourcebook covering the area your current adventure is in, there arent that many spoilers. (I'd equally see no problem with players in a Carrion Crown campaign reading Rule of Fear).
I guess what constitutes a spoiler is somewhat subjective, but in my experience, players with an inkling of what's coming up are far more engaged and less likely to come up with incongruent characters than those who assiduously avoid spoilers of any description.
I think it depends how you define "spoilers." If you want to discover general setting information through the adventure path (e.g., if you want to learn who the Runelords were solely through RotR), you'll need to avoid a lot of products. If you're just looking to avoid spoilers for the actual plot of the adventure path, you don't need to worry very much. Most products may reference areas and characters in other products, but don't reference specific plot elements.
