YES! Gold can tarnish, too. 24K gold is pure gold, but any other karat weight of gold is mixed with other metals. This strengthens it so that it is more suited for life as jewelry, but it also introduces small amounts of metals that can oxidize (tarnish).
The lower the number, ie, 14K, 8K, etc. the more "other" metals are mixed into the gold.
Even lower karat gold, like 10K, doesn’t oxidize easily, but when exposed to gases exuded by tarnish-prone metals, even 22K gold can start to tarnish. My banker told me the sad tale of the customer who had stored gold jewelry and loose coins in a safety deposit box for several years. The copper in the coins worked on the gold in the enclosed area and created tarnished gold and a shocked owner.
The best prevention is correct storage. This is true for gold, silver AND copper jewelry.
Gold is a softer metal and should be stored individually in a box or jewelry bag so it does not get scratched.
In addition, store like metals together: if you store your copper with your silver, it will tarnish faster. If you must store for long periods, separate the different metals and store in sealed plastic zipper bags.
There are little paper tarnish strips you can buy that last for 6 months to a year that can help, especially with silver.