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. :)

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