Gold-filled should NOT tarnish if it has high gold content.
Whether or not gold jewelry will tarnish will depend on how much of the piece is pure gold and how much of it an alloy. Pure gold doesn't oxidize or corrode, but because it is extremely malleable, most jewelry is made of gold and an alloy such as copper, nickel, or silver so that the piece can withstand everyday wear and use. It is the additional alloys that cause a gold piece to tarnish.
The higher the gold content of a piece, the least likely it will be to tarnish. Gold is rated in karats, so the higher the karat, the more gold the piece contains. For example 24K gold would be 24/24 or nearly 100% pure. 18K would be 18/24 or about 75% gold 25% alloy. 14K gold would be 14/24 or 58.3% gold 41.7% alloy and so on.
Unlike an alloy, which is the combining of gold with another metal, a gold-filled item is one that consists of a base of harder metal that has gold mechanically bonded to the surface through the process of soldering, rolling, or drawing. So again, in the case of a gold-filled item, the rate at which it will tarnish is dependent upon the karat rating of the gold portion of the piece.