I have a few 12v LED lights that run off cigarette adapters. I wanted to be able to use my 18v drill batteries so I pulled the guts out of an old charger and added a cigarette socket. The lights work fine on 18v and are rated 12v-24v. My question is would adding a regulator to limit the voltage 12v give me longer battery life or just be wasted as heat?
If you use a switching voltage regulator you will give you about 40% longer battery life.
A linear regulator will not. 30% of the battery energy will be wasted (LEDs may be brighter).
How much you extend the battery life depends upon the voltage and current draw.
When the battery is fully charged the efficiency is nearly 90% for the chip used in this example circuit. It is important to use a regulator that is tuned to your requirements for maximum efficiency.