Wouldn't the second loop fault (with the first already inop) in fact give you a fire warning?
Modern engine fire detection systems are capable of determining the difference between a fault and a fire by the rate at which the resistance/capacitance in the loops changes.
Regarding engine parameters... Unless we're talking about a turbine overheat detection system, most fire loops will only really tell you what's happening on the outside of the engine (in the cowls). You may have have a raging fire in the cowls long before there are any signs of engine parameter changes.