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

If a larger cable sounds different, that is because the smaller cable was not letting everything get through.  I always laugh when someone tries to say a smaller cable is better in their system....that's saying they are like the truncated sound better.

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.