Yes - potentially. Like any compensation event (positive or negative) it is assessed on its own merits using Defined Cost. If both Parties agree, for any one single issue you can use activity schedule rates to assess a compensation event - otherwise it will be Defined Cost i.e. schedule of cost components. What you allowed for is irrelevant. It will be good news if the cost is less than you allowed, and bad news if it is more than you had allowed.
If however they assess it at a figure that is in excess of what it would have cost then you can challenge this, but (unfortunately) only officially through adjudication. I say unfortunately as unless this is for a big sum of money you are unlikely to push it that far.