This is a pretty ugly hack, but maybe it will inspire you to something better.

    leastCJK = ToCharacterCode["⺀"][[1]];
    StringMatchQ[#, _?(ToCharacterCode[#][[1]] < leastCJK &)] & /@ 
      {"a", "1", ".", " ", "中", "あ"}
>     {True, True, True, True, False, False}

Note: "⺀" is unicode character U+2E80, CJK RADICAL REPEAT