Most of the job ads I've seen say they require a TEFL or CELTA, so it sounds like a CELTA isn't an absolute requirement even though it's preferred. They'd probably ask you some questions about your TEFL program to get a sense of whether they'd accept it (what did it cover / how long did it last / was practice teaching involved and with what student population). They probably won't value 4 years with South Korean students as much as they would 4 years with Spanish students because they are very different contexts, but they certainly ought to understand that those 4 years are worth something since to a certain degree teaching is teaching and kids are kids. There is a big market for teaching young learners (i.e. kids), here in Madrid at least, and you ought to be particularly marketable for that because of your experience. Ultimately, in my opinion, the two most important qualities in the EFL market are being a native speaker and having working papers (in that order, with being a trained teacher as the third most important quality) and you have both of those qualities, so I should think you'll be fine. As you've probably heard, the biggest hiring season is September and the second-biggest hiring season is January - come at one of those times and I'm sure you'll get plenty of work. Come at a different time and you'll probably still get work, it'll just take longer. Good luck!
