It'd probably require at least the Hiragana and Katakana, with the Kanji as a bonus if it's possible without too much hassle.
P.S. It shouldn't be any extra hassle, actually. ^_^
Yes, I quote Wonkyth. To be honest, I'd personally prefer using kanji over syllable-only dialogues, but it'll also depend on font resolution and such. Technically I wouldn't know how to make it work, probably Wonkyth himself would be more of help there. There should be some gothic.ttf thing making the magic happen. Adopting sprite fonts in place of proper ones would also be feasible for hiragana/katakana, but close to unfeasible for kanji.
Oh, briefly explained, Japanese has two alphabets (hiragana and katakana), consisting of syllables and vowels, through which you are able to express (and of course, write) everything. Most of the words also have some kanji (ideograms) accompanying them, which helps to disambiguate polysemic words, allow for faster reading, and also decorate the text. Technically you can write everything in hiragana/katakana (as most famicom games did), but using kanji would be better. Say, for example, you have the syllable 'ka' appearing in a text, then it could mean 'mosquito', or 'fire', or it could be just a particle, or a counter, and so on. You should understand the proper meaning from the context. Now, put the mosquito kanji in place of that syllable and there you are, it was a mosquito after all.