It wont cut down on the amount of time that the pump runs, it will condense the run time. The expansion tank is basically a tank with a balloon in it. When you turn on the faucet the balloon starts pushing water out of your faucet. When the balloon has expanded as much as it can and the pressure switch on the pump falls to the predetermined pressure the pump kicks on. When the faucet is turned off the pump fills the tank compressing the balloon and the pressure builds until the switch shut off pressure is reached.
Instead of the pump doing short little on and off bursts to keep the lines pressurized, it now has a cushion. Like any other motor, it's best to turn a motor on and let it run and not cycle it on and off. Even with that said, RV pumps do hold up well and last a long time when cycled on and off.
I installed one along with two GE/Home Depot water filters. At the same time I plumbed the system so that the winterizing port/hose can be put into a 5 gallon water jug and pump into the fresh tank. I dont have to lift any water jugs now.
One way to save battery while boondocking is to not pump water. I have used water straight from a 5 gallon jug instead of putting it in the tank and pumping it.
As Smkettner said, LED bulbs make a HUGE difference in amp draw. I would say they are the number one thing to consider for energy savings.