Quickie
Colonel
Exactly, the AL-31 has plenty of power for the J-15, and when you are staying local and shooting touch and goes off the boat for carrier quals, no need to light the burner as you are already at flying speed, and you willing be staying in the pattern at low altitude, with a visual on the boat.
It might as well be the case as you described, but if the touch-and-go was also part of the training of an aborted landing maneuver, the J-15 speed on contact with the carrier could well be at, or near the trapping speed, to simulate as near as possible to an actual attempted landing. And then to continue simulating with an aborted landing, the J-15 would still need to increase engine power to accelerate to takeoff speed from the touch down speed.
So, the bigger the difference between the touchdown speed and the takeoff speed, the greater is the challenge to bring the aircraft to takeoff speed, and this depends much on the engine power and its spool up time as well.