It depends alot on the properties of your aircraft and what speed you are flying at.
An aircraft has what is called a drag curve.
An aircraft requires an upward force named lift to fly.
Your wings generate lift and by this process occurs induced drag, which is highest at low speeds and decreases with increasing speed.
The heavier your airplane, the more lift you need to produce to balance the added weight, so you produce more induced drag.
By increasing drag, you dissipate more kinetic energy, which means that depending on descent profiles, aircraft, speed and air density the given assumption may not be correct.
Too many factors, it should be studied case by case, which makes the assumption totally irrelevant.