From experience of digging it out or rather trying to I would say yes it can grow back from a small piece of root.
Burdock is a bi-annual so what you will get from your bought root is a plant that flowers and then dies. You'll need to save seed and replant to get any edible root.
them good ole boys were drinking whiskey and rye singin' this'll be the day that I die. Drink tiny ad.
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