According to IGN you will actually need the hard disk drive to be able to fully play this game..

Just like the PS2 and PC players, owners of the Xbox 360 version of Final Fantasy XI will be able to play along with all versions of the game and even use their PC accounts on this version. However the word from IGN is that you'll need an Xbox 360 with a hard drive if you want to play the game.

Thanks BoomTown