That’s not really how it works. The components of the scale require a certain amount of current especially if it’s digital in nature. As a battery approaches being drained, it produces less current. Less current can often power an analog device to a lesser degree, like lighting up an indicator light or LCD or even the IR LED light on a remote, just very dimly. But the tolerance of the weighing components is probably much less than the tolerance of the LCD panel or LED bulb. So many devices use an LCD or indicator LED bulb to show that the device isn’t necessarily broken, it just needs new batteries.

If it’s sitting in a drawer and getting drained, then it’s probably not turned off properly or it may be the type that turns on automatically when it gets pressed down and inside the drawer it’s getting activated. Instead try taking the batteries out of any device that sits around for a long time without use. It will prevent accidental draining and also reduction the likelihood that the batteries will leak after a time. I usually pop the batteries part way out or put them in a small bag that I attach to the device with tape or a twist tie. Just make sure they aren’t touching anything metal and that the poles aren’t touching each other. Batteries will lose charge over time, but with alkaline batteries, that’s usually years, not months. Rechargeables generally take much less time, though.