I think the every part of the game can be played with the keyboard alone, not sure about using items outside of battle or viewing Pokemon stats though.
However the mouse is missing one essential thing, and that is the ability to move the player character. Sometimes when I'm lying in bed, half awake, just topping up some EVs I just want to use the mouse rather than having to lean over and use the keyboard all the time, yes I'm lazy, but I imagine a lot of people are and games like this should be relaxing as well as intense!
Mouse movement could be quite simple and easily disabled in the settings menus for people who disagree. To move the player character up, just left/right click and hold above the character, to move right, click and hold to the right, etc. Whether it's left or right click could be set in the settings menu too, I'd prefer left click.
Also if the player was to click and hold above the character, but then decide to turn right, the player should be able to keep the button held in and just drag the mouse to the right in order to change direction, same goes for other directions. An auto run feature both both mouse and keyboard movement would be nice too.
This would be very easy and convenient to use and it's also a step towards touch screen support for laptops and tablet PCs capable of running PokeMMO.