No, it's an AC current (basically broadband noise). It provides no overall power, and further it's impossible to rectify it into a DC current with a diode at th

No, it's an AC current (basically broadband noise). It provides no overall power, and further it's impossible to rectify it into a DC current with a diode at the same temperature (this is similar to why a wheel with a ratchet, even if microscopically sized, cannot extract work from the motion of particles at a constant temperature).