I assume you've selected Korean as the OCR language, and your originals are of a high enough resolution that OCR is not a problem.
I don't have much first hand experience with OCR'ing Korean language files in Acrobat, but so far it all worked reasonably well.
However, even though it's OCR algorithm is pretty good for "straight forward" files, when it comes to more challenging OCR jobs, I use Abbyy FineReader, which does a better job with documents that Acrobat cannot correctly recognize (e.g. two or more languages mixed in the same document). You may want to try a dedicated OCR application to see if you can get better results.
PDF files are not suitable for translation purposes. Attempting to do so would cause in a lot of problems and headaches.
You need to ask for the original file used to create the PDF, translate it, and then generate a new PDF file from the edited version.
You were right. The thing is the PDF I used was very straight-forward (no pictures, boxes, images. Just a single page of text) which I was told crobat could handle (but it couldn't). I also tried to ocr an English PDF (similar complexity) using acrobat and it couldn't even properly export that either and turned out all broken again. Very disappointing. Anyway, I guess I will just have to use Abbyy for everything to be safe.