No, by default, the application doesn't have support for Korean characters, but this can be fixed easily using a package. Access the URL below, and download the necessary package, then proceed to its installation. Make sure that Adobe Reader is closed while this operation is active. Reboot the PC after it finishes and then open the file with the characters and it should work.
Download page: http://www.adobe.com/support/downloads/detail.jsp?ftpID=4882