Can you study there? Absolutely. I hear the books and materials are mostly in English so doctors are supposed to be able to have a good understanding in English. If you can get into a university over there, I say go for it.
Can you become a doctor there? Unless you are fluent in Korean, I'm gonna say no. Koreans are hesitant about using English in an English class, and if you're a foreigner, many will become uneasy, because they will assume you probably don't speak Korean well (If at all) and choose a Korean doctor over you. They don't want to go to someone they can't discuss their problems with. Honestly though, would you?
I lived there for 4 years, and I don't remember seeing non Korean doctors. It was also a bit of a challenge (not impossible but hit or miss) finding doctors who spoke English. Most claimed they did, but when it came down to it, they were either too nervous or couldn't. I interpret this to mean that real English skills aren't typically seriously considered in the medical field. I only say this to emphasize how much I believe you need to be fluent in Korean. It may be changing now, as Koreans are taking English more seriously, but I can't say with 100% certainty.
I don't say this to discourage you, but this is honestly how I felt while living there.
One more but of advise; honestly do a year abroad working there as a teacher or something before committing. I loved living Korea, but the work culture is intense. Studying abroad and working abroad are completely different.
