No, you dont need a korean sc version. You need a program called gamei launcher that will add Gamei Server I, Gamei Server II, Gamei Server III, Gamei Tournament Server, etc., to your list of servers on bnet.
Once that's done, you need to go to their website and register an account by filling out the form. The form is in Korean however, so unless you can read korean or already know what each statement of the form is asking for, you can't get an account.
The form's quite complex and require you to know a korean residential code (zip code) as well. So either find a zip code not already used somehow, or get a K-Code generator that will randomly list residential codes you can use.
All this said, I want to add that the Gamei server is hardly worth the trouble, people there are more polite (or it could just be that I don't understand them and dont know if they're insulting me), but the level of skills in gaming isn't an improvement over bnet server as you might think.