To answer your question: I personally have seen a Crossfire not want to start even after disconnecting the siren under the cowl, but then, disconnecting the battery for about 30 seconds and reconnecting ( this no power situation will reset some of the cars electronics to default ) the car started right up and was fine after that. The two leads from the car were not touched together, just the negative cable was disconnected.
Your problem may not give the same satisfactory results.