Is Mulan-themed Szechuan McNugget Sauce really just a blend of BBQ and S&S?
See related question on Skeptics, which is basically a continuation of the original of this answer: https://skeptics.stackexchange.com/questions/38472/was-a-package-of-mcdonalds-dipping-sauce-just-sold-for-almost-15k
EDIT:
Was the 1998 Mulan sauce a mixture of McDonald’s sweet-and-sour sauce and barbecue sauce? The world may never know. But since Rick and Morty has endorsed this cooking video from Binging with Babish (the endorsement is here in the description), and I suspect the makers of Rick and Morty are pretty cozy with McDonalds, maybe Babish knows something the rest of us don’t.
In the video, Babish mixes two parts McDonald’s sweet and sour sauce with one part McDonald’s Tangy BarBeQue sauce. He declares it not bad, but not as good as the following:
He really likes the sauce he made from a recipe from a Reddit user, who created the recipe with his father in an attempt years ago to duplicate the Mulan sauce. The video doesn’t give measurements, but luckily I was able to track down the original Reddit post  and the recipe.

•  Mince 6 cloves of Garlic and sweat (heat them up in a skillet)
•  add 4 tablespoons Balsamic Vinegar
•  add soy sauce to taste (DO NOT USE LOW SODIUM SAUCE)
•  add 2 tablespoon Plum Sake (Drink additional 3 oz Plum Sake)
•  Reduce sauce slightly (Drink additional 1.5 oz Plum Sake)
•  3 1/2 tablespoons cock sauce (Sriracha)
•  add 2 tablespoon brown sugar
•  Red pepper flakes to taste
•  Minced Ginger to taste
•  Consume remaining Plum Sake
Simmer that shit for a solid 5 minutes, stirring pretty much constantly. The brown sugar helps it keep the proper consistency, so it's important to use. Play around with the recipe to your taste. Might want more or less balsamic vinegar. Might want more or more Plum Sake. I'd definitely recommend you make it several times to figure out your own flavor.

The rest of this answer is as it was before I knew for sure that the Mulan sauce package in the news recently was a hoax See https://skeptics.stackexchange.com/questions/38472/was-a-package-of-mcdonalds-dipping-sauce-just-sold-for-almost-15k
TL;DR
According to the labels on the sauces, the answer to your question is no, McDonald's Mulan SzeChuan Teriyaki Dipping Sauce is not a mixture of McDonald's Sweet and Sour Dipping Sauce and McDonald's Tangy BarBeQue Dipping Sauce. I say that because because the sweet and sour sauce lists &quot;apricot purée concentrate and/or peach purée concentrate&quot; as its third ingredient. The Mulan sauce does not list that as an ingredient at all, so the Mulan sauce doesn't contain the sweet and sour sauce.

That should be it, right? This is where it gets weird.
The first thing I looked for was a list of ingredients for the sauces. I couldn't find that as text anywhere, so I looked at images of the actual sauce containers. I quickly saw that I wasn't going to have any problem reading the ingredients from pictures of the packages. I choose the first two images randomly. Notice that they're from completely different sources.

From: TheEater.com
And

From: Mouthful of Sunshine
There are two very weird things here. These are supposed to be pictures of the Mulan sauce package and the BBQ sauce package, respectively.
The ingredients on both packages are identical:

High fructose corn syrup, water, tomato paste, grape vinegar, distilled vinegar, salt, soy sauce (water, wheat, soybeans, salt), food starch- modified, spices, dextrose, soybean oil, natural smoke flavor (plant source), xanthan gum, caramel color, garlic powder, cellulose gum, dried chili peppers, malic acid, natural flavors (fruit and vegetable source), onion powder, sodium benzoate (preservative), succinic acid

But that's not even the weirdest thing. Got your tin-foil hat?
Look closely at the two images:

They are the same photo of the same package, with different sauce names Photoshopped in and the color manipulated.
Now that my mind had been totally blown, I looked for other images of the packaging of the sauces that didn't seem to be manipulated. I figured one of the packages above listed the wrong ingredients. Well...

From Popsugar.com
and

From An Immovable Feast
Full-sized, you can read the ingredients on both. They are identical to the other two.
So, either (a) McDonald's had a massive labeling error that would have cost them millions if caught at the time, or (b) the Mulan sauce is actually made from the same ingredients as the BBQ sauce, in the same order of quantity (so, very likely identical sauces), or (c) something is afoot.
I am going to get to the bottom of this with McDonald's, I am starting an email campaign now.
For the sake of completeness, the sweet and sour sauce contains:

High fructose corn syrup, water, apricot purée concentrate and/or peach purée concentrate, distilled vinegar, soy sauce (water, wheat, soybeans, salt), salt, food starch - modified, dextrose, soybean oil, xanthan gum, spices, sodium benzoate (preservative), natural flavors (fruit, vegetable and plant source), garlic powder, cellulose gum, dried chili peppers, malic acid, onion powder, extractives of paprika, succinic acid


From Craveonline.com
This video gets into the lore of the new-found interest in McDonald's Mulan sauce. The video repeatedly refers to the Mulan sauce as only available for a limited time. Hmm. Scratch the surface of the &quot;Mulan&quot; name, the BBQ name might be underneath.
I suspect that the reason the photoshopped image exists is that it was used in a pitch, showing how easy it would be to fool people into thinking that McDonald's created a sauce, available for a limited time only, to tie into the Mulan movie.
EDIT
I just noticed this!:

Now I'm really at a loss.  Even Time missed that date. A new Mulan movie is scheduled for 2018. Is this whole thing a marketing gimmick? The Mulan sauce had been discontinued for a very long time by 2011.
I tried to read the copyright date on the picture of the container in the hand, but couldn't. The printing looks suspiciously like the photoshopped C2011 package, but it's either not the same package or it has been further Photoshopped since the lower left hand corner is clearly different.
I find this whole thing very mysterious, so I will continue the investigation. I think I'll ask the folks at Skeptics for some help with this.