Yes, it is supported. Several different legacy Japanese character sets are supported (JIS, Shift-JIS, EUC, and even UTF8). Internally, AbsoluteTelnet is Unicode-enabled, so these legacy character sets are translated into Unicode on the way in. On the Options->Properties->Appearance page is where you set the character set to match the character set of the data on the host.
AbsoluteTelnet has support for the Windows IME (Input Method Editor), which is the way Windows apps support keyboard inputs from multinational keyboards. Using the Japanese IME, you can type Japanese (assuming you know how to type japanese) You must install language support under the Windows' control panel 'Regional' settings before this will work, though.
To test the Japanese capabilities of Absolute, you must have some source of Japanese text on the remote host. try installing the japanese man pages, for example. See this image for an example:
Or, install a UTF8 enable newsreader or mail client. It all depends on what you want to do. There are resources on the NET that describe how to do all these things. If you need further help, let me know.