although there are a few random events that are related to natural disasters, at least two of them are drought/famine related, but they kind of hint at the disaster happening on several planets at once, which doesn't make a whole lot of sense, there is one or two meteor shower events, one event where a moon or some huge object is going to crash into a planet and the race that are the victims (some minor race incapable of interstellar flight I guess) are the ones that you have to save. Theres also an interstellar plague event.
So there are a few random events related to natural disasters which would be significant. Things like tornadoes, quakes, volcanoes, and hurricanes would be something localized and the planetary government would take care of it.
However, if it was something very severe like a Krakatoa or Tambora sized eruption which would really wreak havoc and would require some outside help, that could be an event.
When you have a huge number of planets, approaching 100 or more, then chances are that at least one could have some big local disaster at any time. But the majority of the random events are related to military, political, research, or morale things.