No, you need to have firmware version 3.55 to install 4.31 CFW.
If you are not on 3.55, then you need a hardware flasher to downgrade.
Source: Consolecrunch
@Xdqwerty, Osu! Tatakae! Ouendan! is the Japanese version of the game, different settings/characters/songs but otherwise identical mechanics. I played that before I knew about Elite Beat Agents lol. Both fantastic games https://en.wikipedia.org/wiki/Osu!_Tatakae!_Ouendan