No. It is not the takeoff as in "raising the wheels from the tarmac" part that is consuming most energy, but reaching the flight altitude. Real case, with smaller plane, I take off in 300 meters in less than 30 seconds at max power, than raise to 3000m in more than 10 minutes of 90% power. That makes the assisted takeoff less than 10% of the energy to get to cruise altitude.

I don't have the numbers for a jet fighter on a carrier, but I think it is in the same range. The takeoff assist is not for saving fuel, but to allow takeoff at the loadout of the plane that would require otherwise a longer runway or lighter loadout (less fuel and weapons).