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

This is an area that cable geometry can make a difference.  I would suggest listening to several cables and go with what sounds best.  

You have to remember that not only speakers but to a lesser extent cables exhibit impedance, and together they form a impedance circuit. 

 To lessen that effect use thicker/lower gauge wire.

From Roger Russell (former McIntosh Director of Acoustic Research)

Wire Table

This is hard to beat.

Wire Gauge: 16 AWG
Capacitance: 35pF/m
Inductance: 0.52 µH/m

I needed some slightly longer cables as a new amp wouldn't fit in my normal amp rack space and needed to be a little further away from the speakers. I saw the new version of Kiimber 8PR cables now using the "varistrand" design (varied thickness little solid core wires in each strand), liked the look and paid less than 500 bucks for a terminated 13.5 foot pair. They look great and sound great...10 AWG to each speaker post.