The answer to the question is not really.
However, sentences two and four are correct.
I do not know what sentence three was supposed to mean.
But can sometimes be used instead of 'except.'
It can also sometimes be used instead of the expressions "apart from," or "other than," which are also similar to "except."
In sentence one, above, you could say:
1) I have never been abroad, except to South Korea.
2) I have never been abroad, other than to South Korea.
3) I have never been abroad, apart from to South Korea.
4) I have never been abroad, with the exception of South Korea.
But saying "I've never been abroad, but to South Korea," would sound strange.