[AndrewC]

If sufficient power was produced the reactor would have lost moderation and reflection, resulting in a shutdown. Until shortlived fission product poisons decayed away, even immediate re-saturation may not have resulted in restarting the nuclear chain reactions. Therefore, the reactor probably did not operate continuously, but at discrete intervals with the operating time determined by the power output, water supply pressure and temperature, and water flow through the reactor. The duration of the shutdown periods would have been determined by the buildup of fissionproduct poisons and the length of time required to replace the moderator (if it boiled away) or to cool it sufficiently to resume the reaction.

[Doctor Stochastic]

The question was whether a nuclear reactor could form by chance. Whether the (hypothetical) reactor is/was intermittent is interesting, but not what I asked.