No. You are only doubling the ABILITY of the motor (alternator) to produce electrical power. The alternator only puts out as much current as is being demanded at the time. If you have no accessories turned on, your alternator might only be putting out a few amps to run the computer and charge the battery. If you crank on all the lights, the HVAC fan, the stereo, and the electric cooling fan kicks on, your alternator might be putting out something like 150 amps. If this demand exceeds the capacity of the alternator (at the RPM it's running), then the extra current is drawn from the battery (discharge).

You are going to rob power from the motor. The more current put out by the alternator, the more power it takes from the motor to produce it. It has nothing to do with which alternator you put on the car, it has to do with the fact that you are asking the engine to convert more of its power into electricity, rather than putting it to the rear wheels. You have chosen to put high electrical demand items on your vehicle, and the power to run them has to come from somewhere
Power (watts) = amps X voltage
A 200amp alternator that is putting out 100 amps is putting out 1.4 kilowatts. 1KW = 1.34 hp, so it's taking almost 2 hp (not including mechanical losses) to make that 100 amps.
If it's putting out its maximum 200 amps, it takes 3.8 hp. To account for mechanical loss, you should probably double that.
So you are losing 4 to 7 hp at the flywheel, and whatever that translates to at the rear wheels.