Bale processor or not, it looks to me like asking for trouble if the net wrap isn't either all picked up or completely shredded. Getting it wrapped around bale processor parts doesn't sound like fun either. If a cow got that stuff stuck in her throat and it wouldn't go up or down just doesn't sound like a good thing at all.
FWIW, my disclaimer is I have never been around net wrap at all, so maybe I'm all wrong. I use sisal twine and don't worry about it after a season. I do try to pick up all the twine from first season bales I feed. I just unroll the bales on the ground.
I have considered a bale processor also but then I get to thinking about the $$$ they cost and the fact that when the weather gets bad it would be like dragging a big anchor around in the snow.
I'm sure bale processors have their place, but I feed my cows with a $6K 130 HP tractor and dozer with a $600 bale unroller on it. IMO, it's a pretty capable feeding rig for the $$$ invested.