Question regarding Application data and DLC

So, I am a new ps4 owner. And as such, I have recently discovered that DLC data is integrated into the game data itself, which is frustrating. It's a nice change from ps3 to be able to backup saves without having to back up the entire hard drive, but it would have been nice to be able to backup up just the DLC as well. So my question, if I were to redeem for example, Day One Edition weapons/costumes etc, and then delete my game data, and once again reinstall it, will I be able to load my game save? As I understand, with something like a story/mission based DLC, I would not be able to load it if I don't have that particular DLC installed (Or is that not always the case?). I'm just trying to understand this a little better. Any assistance is appreciated, thank you.