In the health care sector, there is always a need for an Interpreter or a Translator. Commonly I've seen the demand for Japanese and Arabic languages. Although not very common, but I have come across Korean language clients needing translation.
Are you doing this for having an another degree or planning to emigrate or work as a marketing consultant or stay in Korea? If so, go ahead. If you are learning it for translation jobs, Please analyse the supply and demand for Korean language. If it's Japanese,German, I would say yes.
The Jobs after foreign language proficiency is in the translation sector, interpretation needs in meetings and medical care, Emergency interpreter on call for international hotels, airports, MNCs that deal with clients from Korean etc. The next would be private tutors of Korean families in India or in Schools to help with education needs of Korean students.
I would suggest talk to people in this field and a then decide. You can try contacting the hiring agencies who can give you a realistic idea of what is the scope, the pay and even other alternative languages.
If you are learning a language for just the desire to learn, then go ahead.