Sure it would. You can say that one ounce of gold can be exchanged for $1000 U.S. dollars but elsewhere in the world the market price of gold will fluctuate with supply and demand.
marron is correct. The price of gold in dollars would be the same no matter what country you were in.
The price of gold and the value of the dollar would adjust in tandem against the local currency. The value of the dollar in terms of gold would remain constant.