I've never met a Carolinian that didn't have a strong opinion about sauce, or anything for that matter, myself included (born and raised). You stumbled upon one of the great Carolina debates, like college basketball in the middle of NC. This doesn't even address the whole hog vs shoulder issue. When people say "Carolina Pulled Pork", it's like using the word "BBQ" to describe smoking, grilling, a party, and/or the actual meal. Over time I guess words just evolve into something else.
I tend to cook whole hog (extra shoulder mixed in) and "sauce" when flipping the hog skin side down later in the cook. It adds another dimension of flavor. I use an Eastern NC / Northeastern SC style sauce, which always has a base of vinegar (white, apple cider or mix), pepper, worsty (or some type of fish or oyster sauce), salt, and red pepper (usually crushed). I add honey to mine.
In NC there are traditionally 2 primary sauces, both thin vinegar (tomato in the west, not in the east), and Raleigh/Durham is a free for all. And, yes, there are traces of mustard in NC. Fun fact...people used to think tomatoes were poisonous and traditionally ketchup (catsup) was simply a vinegar/pickled fish sauce with spices, and sometimes mushrooms, but not tomato. Certainly puts an interesting twist in the debate.
As to SC, there are at least 4 major types of sauce, mustard based, vinegar, tomato vinegar, and ketchup based. Being a central SC native, I love the mustard based sauce, but caution there's a lot of bad versions out there, just like the ketchup counterpart. I believe it came from German settlers when they migrated up the river systems from the coast to the central part of the state, (pork, mustard & cabbage...sound familiar?). I'm now in L.A., via a half decade in Philly, and my mustard sauce has always been everyone's favorite. It's great not just on pork, but briskey, smoked chicken, veggies, etc. My wife loves to pour it over grits, fried egg & briskey hash.
As to your original question (sorry, I get a little carried away), when I pull/chop I add my vinegar sauce to flavor. Initially, it may seem wet, but I pour until it hits the flavor I want. It will take a little more than you think b/c when hot it seems to absorb the vinegar sort of like a brine. It also keeps it moist for low-temp reheat so you won't need to add any additional later. I read once in cooks illustrated that vinegar absorbs better when hot, but this was for a potato salad test so not 100% sure if meat fibers would work the same way. This gives the best of both worlds, pork flavor with a little tang, and some smoke allowing any other sauce to compliment it. Traditional "Carolina BBQ" actually isn't very smoky, and doesn't need to be. I assume adding the mustard sauce will have a similar affect, vinegar being a key ingredient, though it could slightly alter the effect of poured side sauce.