Can I work in the U.S. on F-1 status for a company registered as a business in Korea?

Is it possible for a college student currently in the U.S. on an F-1 visa to earn money doing paperwork/office work in the U.S. for a company registered as a business in Korea?

The wages are paid into a Korean bank account, and taxes are also paid in Korea. I’d like to know if this could cause any disadvantage later when applying for a green card or citizenship.