OP : Yes, wire gauge can (in theory) impact voltage at the load. A perfect wire has no voltage difference, and would have the same voltage at the load as at the source, whether we are talking AC power or speakers.
In AC power transmission in a home, 1-2 V per leg loss is normal. Meaning, 2-4 V drop at the appliance relative to the panel. A higher gauge wire than required can reduce this.
As I mentioned before, the voltage loss (i.e. drop) is proportional to the current. It is also proportional to the wire length. For the same wiring, a high current device on the end of a long line will suffer more drop vs. a low current or short run.
For speaker cables it is extremely rare to expect voltage drops more than a couple of tenths of volts with anything equal to or better than 14 gauge cables.
