No, because it reduces fuel flow into the combustor. Torque is just the end result, but it's also going to keep temps from going high.
Also, it's not instantaneous, and during my initial training I discovered that while the PCL lever in the Simcom FTD is pretty well instantly-responsive, if you try to just throw the lever forward in the real airplane, you will bump it over the torque limiter and it takes a moment to recover. That's why there's a 63.3 or some somethingish for 5 seconds limit on the torque gauge. But I never saw it get that high, and it never went that long. Also, I've only taken off from APA twice in the summertime, first time without ECS on, second time with ECS on. We self-limit our takeoff roll to 36.9 PSI unless it's absolutely necessary to use full power, and on both rolls through the initial climb, until I could gain a bit of airspeed, the temperature was in the 730/740 range. The only real difference the ECS made was when I turned it on during the climbout it bump-dropped the cabin altitude even though I set the cabin altitude to 10k, because I didn't want the bump and wanted to bring it in gradually, but I can't have nice things. So the second time I just kept the ECS on.