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

Generally, yes.

ozzy

Why?  The current involved is miniscule.  It would decrease resistance but increase capacitance. 

My general feeling is that speakers and amps are a little more susceptible to LCR effects than we give them credit for. 

Meaning, cables matter, BUT... it's really small changes. So, possibly, but I wouldn't pay a lot for it. :)

My favorite all around cable is Mogami which is pretty affordable and comes in a couple of different gauges, including a quad you can put together as ~ 10 gauge.

+1 @ozzy

Given the same material, yes, most likely. I did some comparisons long ago using power cords cut to be speaker cables.

Are you going to hear it? It depends, how resolving is your system? How experienced are you in listening?

Now if you are comparing different audiophile speaker cables, then it competely depends on overall construction… dielectrics used, geometry… stranded vs solid… etc.

Why? There are many threads on the subject. 

If you’re running the recommended size and go to a much larger size, I would say no. If you’re running some thing that’s way too small and then you go to what’s recommend it then you might.