Anecdotaly, I have a remote that lights up everytime it's moved (to assist finding it at night as it's a remote for a bed). I've had it for well over a year and haven't changed the batteries yet. Granted, it runs on three AAA batteries. Not entirely sure what tech it uses, but it's not necessarily a full blown accelerometer.

Edit: some / all of the power drain would be offset because the RF transmitter would be off while the sensor is on.