If their parents both carried the necessary genes, then yes, it's possible. The most likely senario, though, is if both parents were half Korean, half European - this would double the chances of blue eyes - given that blue is a recessive gene.
Eye color is actually controlled by a group of genes, not a single gene pairing (one from Mom, one from Dad.)
I have dark eyes and dark eyes; so does my husband. I have two dark-haired, dark-eyed children and one blond with very pale blue eyes. My parents were dark; so were my husband's parents. We scratched our heads a lot when I had a little blond girl.
And that same blond girl is married to a dark haired guy and they have a little redhead, almost a carrot-top.
Genes and how they are expressed are funny things. Many of them work in groups. The ones Mendel studied were fairly simple. Two dominant reds, you get red-flowered pea plants. Two recessive whites and you get white. A red and a white, you get pink. Not every organism works quite that way, however.
I'd still just go with having some of the characters dye their hair. It gives you the color you're looking for without having to haggle about the genetic details or possibly insulting someone who thinks you don't know your genetics (and thinks you should.) You don't need to know anything about inheritance if your characters dye their hair.