I don't think it would work if Barney left - the constant cock-ups, terrible cheesey lyrics, etc are what most of us have come to love as 'classic New Order' 
However, if the question had been: 'Who do you regard as the most EXPENDIBLE member of New Order?' or 'Who would it be easiest to replace?' I'd have to go with Barney - Hooky's bass parts (when he's allowed to play them or they're not 'dumbed down' in the mix) are brilliant even now - listen to 'Dracula's Castle'.
Steve Morris is the only technically excellent member of the band, is creative and was essential to many of the 'classics' that everyone here loves - BM, TPK, BLT, etc.
Barney? Well, there's cheesey lyrics, drunkenly insulting the audience, forgetting the words to his own songs, poor quality vocals - both live and recorded (although they have improved) and the poorest 'side project' of the lot - relying on Johnny Marr to make the songs listenable.
Easiest to replace Barney, but I'd hate to see any of the current members leave. That includes Phil, who doesn't deserve half the flack aimed his way by 'fans'.