Ya they will warranty it for you. You can also try going to a shop near you that sells product that has the BOA wheel on it, and see if they have spare parts. We had a bunch of replacement BOA parts that we just gave to people if they came in, but not all stores have BOA parts.
FWIW, this is the EXACT reason why I personally will never buy BOA boots, and why I steer customers away from BOA.
How do you replace the wire? is there any website with instructions?