For Chinese characters and Korean syllables, the autocomplete should search even when there's only one character. In these scripts, one character represents a whole syllable (and when Chinese characters are used in Japanese, often more than one syllable) which is often an entire word, and that means one character titles are more common. In any case, each character gets far fewer matches than a single character in something like Latin or Cyrillic, because there are thousands of them.
Some examples of artists:
嵐 (Arashi) - http://test.musicbrainz.org/artist/1008b912-cbb1-4e4c-bd4d-b9adf6937e8e
鴉 (Karasu) - http://test.musicbrainz.org/artist/37df5cc9-ec9d-4eb3-93fa-4b0e8806b5b2
虹 (Niji) - http://musicbrainz.org/release/5289f221-6efb-4fe3-9ec4-5186695e339e.html
光 (Hikari) - http://musicbrainz.org/release/8f80a42c-1f1b-4889-ac62-8e54e1f708ce.html
煌 (Kirameki) - http://musicbrainz.org/release/5229433a-cf54-4e0f-84b1-143528f7a867.html
I found this while testing http://bugs.musicbrainz.org/ticket/3337