Nope - price is a function of supply and demand. In your hypothetical, demand stays the same. The supply stays the same, too - because the gold mines are still

Nope - price is a function of supply and demand. In your hypothetical, demand stays the same. The supply stays the same, too - because the gold mines are still limited to the same amount of gold they get out of the ground. So long as the amount of gold is mined unchanged, the fact that the processing is cheaper makes the mine more profitable but doesn’t change the price of gold.