Good news. Theory is confirmed. It works.
Some explanation is helpful. Hangeul consists of a 24 letter alphabet. However, unlike the English/Latin alphabet, it is not written sequentially. It is written in syllabic blocks. Thus, a word like Korea is written as ?? (han-guk). This contains the letter sequence of ??????.
I read through some of the Unicode material on how Hangeul is encoded. It encodes the letters ?? ? as three unique characters and ?, a syllabic block, also as a unique character. This creates an "interesting" problem.
There are more than 11,000 possible syllabic blocks. Though, not all of them are phonologically possible in modern Korean. I believe it still numbers somewhere in the thousands. This means one might reasonably need to create a rather large image file. That would be game dependent of course, but it still makes me a little sad.
For reference, see the following Unicode PDFs.