You needn't do either as long as you have given the appraiser full right to negotiate your claim on your behalf. Therefore, when the appraiser signs the appraisal aggreement, the appraisal become binding. The case will be closed at that point, with the exception of a coverage dispute which can still be litigated. To answer the question, it is held in many courts that the signing of the appraisal agreement binds the loss and, therefore, there would be no further need for a proof, nor would it be important for the check to be signed. Once your representative (appraiser) has signed the agreement, you are bound to that settlement.
Crystal