The input method is independent of the font. Normally it's part of the OS or desktop environment, or is third-party software which integrates into such. (Windows IME, ATOK, SCIM-IM, Anthy, Wnn, etc. are all examples.)
All you need to worry about is adding the Japanese glyphs to the font at the correct codepoints. That is certainly possible in TypeTool.
BTW you should be able to create at least a minimalist Japanese font in FL5, as common-use characters (Joyo kanji plus kana plus Latin) only take about 2200 slots. There are a number of Japanese fonts out there which do this. It doesn't come close to complete JIS-X-0208 coverage, of course, but it'd be OK for most everyday purposes.