No, cancelled checks that refer to a "Payment Stop" order cannot be used as proof of redeeming in lawful money because no funds exchanged hands.
A check which has been drawn or cashed is sometimes called 'cancelled' by financial services, but these checks still serve as proof when indorsed originally with the lawful money verbiage. In common vernacular, these checks, often obtained from the bank's records, are called a 'photostatic check copy' and serve no financial purpose other than for record keeping.