LEDs are diodes. So you can run power _through_ them. Power Supply -> LED -> Camera.
While true, the amount of power would be too low, LEDs also have quite high forward voltage (~3V for blue ones) and they are current driven devices. That suggestion would require pass all the current through the LEDs. LEDs don't like to be reverse biased either. Overall, it's a rather appalling idea. On top of the fact that LEDs can fail short.
More also you'd want a hold up time for the light (few seconds at least), as taking pictures would flash them for 1/60 of a second or so.
They have high forward voltage /drop/ which is a useful property. You drive them with constant current for constant brightness and improved lifespan which is most pertinent for LED light bulb replacements than it is for a simple signal status light. Fixed delay before standby isn't hard to enforce either.
Even so this whole attack vector isn't solved with this. How long should the light stay on for after the camera is put in standby before a user considers it a nuisance? 5 seconds? So if I turn my back for longer than that I'm out of luck anyways.
The anti-TSO means would be a hardware serial counter with a display on the camera. Each time the camera is activated the number is incremented effectively forming a camera odometer. Then if my previous value does not match the current value I know it's been activated outside of my control.