You don't even need the DVD burner - you can use sticky tape[1] (to make graphene anyway). That is actually how it was discovered[2], and that was worth a Nobel prize.
You have no control of the layer thickness through this process, and their supercapacitor design actually uses the graphite oxide that isn't turned into graphite as an insulator between the graphene sheets (their supercapacitor is planar, it does not use multiple layers). So no, while you can get graphene from a pencil and sticky tape, that's useless for this application.