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.
Opportunity is missed by most people because it is dressed in overalls and looks like work - Edison. Tiny ad:
A rocket mass heater is the most sustainable way to heat a conventional home