I've rendered Japanese characters with imagettftext before, by using the East Asian font directly. There are a few which come packaged with Windows : "simsun" (Chinese) "MS Gothic" (Japanese) "Ms Mincho" (Japanese) The last two are the equivalent of sans serif and serif for Japanese text. I think the Chinese ones have both styles too. In my old php code it uses font files with a ".ttc" extension, not sure why. Perhaps TTF is the definition and the actual font is a TTC file? (that was long ago)
Anyway, as for using Arial etc, on Windows at least the way it works is that the system detectes characters outside of the "western" Unicode range, and will automatically switch to one of the default installed "Asian" fonts to render those. Thise cause among other things, some users to get chinese characters instead of Japanese or vice versa, because many of those characters share the same unicode range, but depending on which font is used, you egt the "chinese" stlye or the japanese style.
Mixing both fonts doesn't look great. Using purely a Japanese font will render the alphabetic characters in a "monospaced" font, which doesn't look too good.
If all else fail, you could try to split your string into separate western/eastern character range substrings (loop on characters and test unicode range), and then render each part with the appropriate font. Keep in mind the Eastern fonts are monospaced (at least chinese/japanese, I don't know about korean, etc).