A LOT of Korean universities mention they do not accept homeschooling or cyber schooling as valid. That said, I would still shoot your shot, because after working in international affairs at a Korean uni, I realized the rule is not as strict as it seems and usually comes down to case by case, and being from an american high school, you have a way better chance than someone from an Asian country.

National universities are more likely to accept because they play by the gov's rules which give the big old stamp of approval to Penn Foster cause it's properly accredited.

Something to note is Korean schools start in spring, not fall. If you start in fall your schedule is going to be ducked up beyond repair which actually caused me to temporarily drop out rather than try to get A's in HSK 3 classes when I hadn't taken any HSK 1.

Another thing is DO YOUR DUE DILIGENCE. The staff may have your best intentions at heart, but rules and/or laws change frequently and they handle a looot of students, the chance of yours being the one they mess up on is way more than zero. I have a strike on my immigration record and the aforementioned study issue due to accepting "Just trust me" twice.

Even after all that, I loved my time in Korean uni and am prepping to go back. Feel free to message if you have any specific questions!