I saw Herndon give a seminar on this topic a few years ago. It is a plausible theory, but not an established fact, and not accepted by most in the field. As I recall, we don't understand the earth's core well enough to know if enough uranium could have collected at the center for a reactor to happen. One way of testing the idea is to look at the flux of anti-neutrinos coming from the earth. If the number is greater than can be explained by beta decay of the thorium-chain elements, it would point toward a geo-reactor. I seem to recall that some proposed neutrino detectors have a chance of measuring this. They have to be able to discriminate against the large flux of neutrinos coming from the sun.
An interesting part of the theory is that the geo-reactor proposed by Herndon will run out of fuel relatively soon, so if it exists the earth will lose and important source of internal heat and begin cooling much sooner than if all the heat comes from radioactive decay.
