I just purchased an iCharger 308 duo and a 33amp 10v-18v power supply. I will be charging 2 - 2s 4600mah lipo's at 13.8 amps each. Will the charger or power supply have to "work" less at a given voltage setting? Or does it even matter.

You wil charge 8.4v at 13.8A, that is about 110w

You you will charge 220w, that is 60% of what the PSU can handle