Does Wire Gage have that much importance when going from the line source of 14 gage, to the load source at 12 gage.

Under the National Electric Code, the wire size determines the maximum current-carrying capacity of the circuit. 12-gauge wire in households is normally allowed to carry up to 20 amps. 14-gauge wire under similar conditions is normally allowed to carry only 15 amps.

Wire always has a resistance. As current passes through the wire, some power is dissipated as heat I^2R=Power\,lost. This is accompanied by a loss of voltage. If you have very long runs of 14-gauge wire, the voltage drop will be greater than the same run of 12-gauge wire.

Does Wire Gage have that much importance when going from the line source of 14 gage, to the load source at 12 gage.
To be honest I have no idea what you are actually asking, but YES, wire gauge does matter.

The circuit must be fused/breakered for the smallest wire in the circuit. So mixing wire sizes makes absolutely no sense. In some cases it would create a violation, such as a kitchen receptacle circuit that is required to be a 20A circuit.