I don't think so... think of it this way.

The Chaos Lightbulb is constructed of a normal lightbulb with a built in NOT gate. The fact that no power goes into it undergoes a x=(x+1) & 1 process to create power inside the lightbulb.
However, if you somehow use the Lightbulb as a source of power, the 1 will go through the NOT gate and thus turn into 0, or no power at all. You can't get power from a powered Chaos object, because they are effectively NOT gates. You'd need to hitch up the Chaos Lightbulb to a Chaos Wire, and I haven't seen any of those around, unless you could possibly use the Chaos Coil as one.