The sole purpose of the washer is to sit on the splines and provide a more even surface for the o-ring to crush down on therefore reducing the risk of oil leaking up the shaft.
Is it 'Necessary'? No, not at all. In fact very early five speeds didn't even use the o-ring! Is it a good idea? Certainly, as it will assist in preventing oil escaping from the gearbox into the swingarm. Whether you install one is entirely up to you. On a G5 it won't make a lot of difference. Where it is vital is on machines like 1100 Sports, Daytona's and Centauros where any leakage from the output shaft has the potential to contaminate the rear tyre.
Pete