Would an Apple Watch charge any quicker if connected to a 12W USB power adapter?
No.  There is no quick charging feature on any of the Apple watches.

As far as documentation goes, Apple rarely documents what it can’t do; so you’re not going to find anything official.  

However, with a little bit of research, we can posit as to why Apple’s watch is limited to 5W: physics.  The Apple watch uses an inductive (wireless) charger that’s held in place with magnets and connected via USB (5VDC).  The thing with inductive chargers is that the receiver coils’ (in the watch) power capacity is determined by the gauge of the wire and the number of “turns” which influences the size if said coil. 

In the Texas Instruments paper Designing a Qi-compliant receiver coil for wireless power systems it states that a coil with 5V output at 5W would require a coil with dimensions of 48mm x 32mm with 15 turns (page 4).  Needless to say, thats much larger than the actual watch itself.  The coil in the watch is obviously much smaller with finer gauge wire meaning lower power output.  5W is the smallest USB power adapter they make, so they simply include it rather than create another power adapter specific to the watch (IMO).

This is confirmed with this YouTube video testing both the 5W and 12W chargers.  The charging speed is identical for both meaning the watch won’t “quick charge” with the 12W adapter.  Likewise it continues to show that you can use any USB charger so long as it’s greater than or equal the the power requirements of the device.  You can use a 91W USB-C charger for your watch with no issues (but you shouldn’t the other way around)