To answer your original question, NO, the '03 and '01 are nothing alike in the undertail... the '03's have a removable mudguard, the '01's do not. You'll have to buy an undertail for the '01's if you want to take off the fender completely. Look under yours, you'll see it's all one piece black plastic. The '03's have a color-matched undertail with a small black mudguard piece that can be taken off as described, leaving a nice smooth same-color undertail. Most guys with pre-03's get a nice effect however just by cutting off the excess mudguard below the storage box, and remounting signals and plate.
"Keep yer feet on the pegs and your right hand cranked."