Will increasing speaker cable AWG make a difference in sound quality?

Distilled answer:

Maybe.  Maybe you can hear a difference, maybe not.

With respect to 'not much amps flowing'. If your woofer eats a 200W impuls at 4 Ohm that (read up on Ohm's law) makes it 7 amps. Some speakers dip well below 4 ohm, and some peak power burst can be higher than 200 W. That is the reason why sometimes amps are needed that can deliver lots of amps (pun intended). Not sure how big the differences are in the esotheric heights of $10+/ft price levels, but back when, even the least skilled listener could accurately blind test the 'lamp cord' vs a 4mm2 multistrand even on our  "LoFi" (Audiogon scale) systems. Interestingly, the by far best speaker cable we ever heard back then (and includes cables we would never spend our hard earned money on, but did A/B comparisons in listening rooms) was a coax cable used for cable TV distribution in large complexes (at 50 cents a foot from our wholesaler). Still have a section (40 years old) and eager to dig it out and power my Nautilus 804 with it, see what it does. 

generally yes. Large wire size is required for the high current that flows for small fractions of a second during dynamic changes or big bass notes. a mellow song will sound the same with both but, just like in power cables, there are dynamic times when higher current flows, even if just for a picosecond.  The simplistic calculations like others are doing in this thread are wrong.  It is the google level of understanding physics.  I have a physics degree from UofC.

Changing the gauge, will change the tonal response, larger diameter will shift the tonal response towards the low end and vice-versa.

Whilst increasing the gauge of the wire invariably changes the sound in some way the original post talks about Improving Sound Quality...

Increasing speaker cable size (for example w/AQ the cable sizes move up in size from 15AWG to 10AWG) improve sound quality?

For me - improving sound quality encompases

1. eliminating tonal colourations - i.e getting to a natural sound
   • increasing the gauge will CHANGE the colouration, but will not reduce them
   • this is because the surface area of the insulation that comes into contact with the metal of the wire increases.
   • The Dielectric Constant of the insulation needs to be as low as possible in order to reduce coloration
2. faster dynamics - i.e. crisper percussion instruments
   • this can be achieve by improving the metal of the wire
     • e.g. OCC copper instead of OFC wire
   • OCC solid silver wire provides the fastest dynamics at present
3. improving clarity and details - and as a result, improving image
   • this can be achieved by using a better cable geometry, which reduces the noise actually generated within the cable between conductors
4. using solid wire as opposed to stranded wire - improves clarity and dynamics

NOTE: changing one of the above will improve sound quality a little, but the more things you change the better the sound quality

If you want to read more on this topic take a look at this thread

What I have found makes a good cable

And if you really want to get into the nitty gritty of DIY cables take a look at

Duelund conversion to diy helix geometry cabling

Regards - Steve