If a light bulb is dead, does it still consume electricity if the switch is in ON?
It depends on the type of bulb. 

Regular incandescents won't consume any electricity if the bulb is dead, since there's no continuous path for the current to take. It's just like an open switch.

With CFLs and LEDs, it depends on why the bulb burned out, but in general they will consume some amount of electricity even when burned out. Some CFLs may even consume up to 50% as much as a good bulb (older link, but a lot of burned out bulbs may be old). Newer bulbs may have circuits which eliminate most electricity usage on dead bulbs, as this answer from the electronics stack shows.

Smart bulbs have additional electronics, and so would consume even more electricity than an equivalent non-smart bulb, assuming of course that it's not the smart electronics that died. 

The only way to be sure is to measure the usage, with a device like a Kill-a-Watt meter. You would need to install the bulb in a lamp or other fixture with a plug.