Unless the flight leaves out of the international terminal or it's the same plane, both unlikely, you will have to transfer to the domestic terminal and hence go though immigration and pay. I took a LAN flight to Calama in March and it left out of the domestic terminal. Calama is not the biggest airport and I do not remember them having a customs or immigration area.

P.s If the line is long at the first upstairs "toll booth" in SCL there is another down stairs to the left of immigration.