You could wire it up either way. In general the LED is extremely likely to outlive the rest of the laptop, though.

Yes, and it would die rather quickly if it would be a typical low power 2mA LED. Cam sensors can consume quite a bit of power, certainly more than 6mW at 3.3V when active (easily 200-500mW). Even if it would not die, it would be irritating, because light intensity would vary with power consumption of the sensor module.

Nobody sane would hopefully design it this way. :)