Have you tried to make the purchase to see if it will work? That would answer your question.
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You can only use a credit card in the currency and billed to an address in the country for which you are using the store. If you don't have a Korean card issued to an address in Korea it will not work.
You aren't really supposed to be using the store in Korea if you do not actually live there.
http://www.apple.com/legal/internet-services/itunes/us/terms.html#SERVICE - Jan 2018 "Our Services are available for your use in your country of residence (“Home Country”)."
Used to be:
"Our Services are available for your use in your country of residence (“Home Country”)."... " Any other use of the Services and Content is a material breach of this Agreement. Apple may monitor your use of the Services and Content to ensure that you are following these Usage Rules."
Even older wording was more specific: "The iTunes Service is available to you only in the United States, its territories, and possessions. You agree not to use or attempt to use the iTunes Service from outside these locations. Apple may use technologies to verify your compliance."
Question: I live in the US, and i want to do some IN-APP purchases on a Korean App, but i don’t have a Korean credit/debit card. Can i still buy things without having one?