Artemis
Shouldn't unless it's a gold-alloy, which may contain copper. Cheaper jewelries are usually plated copper, and once the plating wears off you get that lovely green colour. Make sure the anklet is 10k gold, not 10k gold plated. They get tricky like that. If it's real gold it should be ok.

Rosa
i don't think it will unless it's a gold-alloy