For wood to regrow the bark still needs to be around it. If your wood has been through a shredder that'll probably not be the case.
Hand-pruned willow... that would be a different story. Then I would expect lots of twigs and branches with the bark still around it and then in moist conditions it would continue growing.
But you're talking 'chips' so I don't think you have any worries at all. Willow being soft wood, it
should decompose and become food for your plants relatively quickly.