Having lower estrogen levels does not mean that you will see a faster or better change in body composition, or that it will be easier to gain muscle or lose fat. There are many other factors involved. Nutrition, for one. Training, for another.
Another thing is, even if you may have had amenorrhea before, you can STILL get your period back, once your nutrition is on pointe. The primary reason for loss of period is NOT from overtraining, but from lack of sufficient caloric intake - which can be caused by not eating enough coupled with overexcessive exercise causing even more of an energy imbalance, or just being plain stupid re eating habits.
Some things are not as simple as black and white; there are many things to take into account.