Yes.
AI's can unlock Colossi, which require you to pick a weapon type via event. Furthermore, the Ascension Path's (at least Synth and Psionic) are event based, and AI can complete either. As well, Glavius' AI mod mostly uses AI-only events to fix AI missbehavior.
However, it's fair to reason that there are a lot player-only events. The most obvious one (prior to 2.2) was the Piracy Spawning event.
So chances are the AI's can not gain the same amount of events as players can (and given the intent of the game to entertain players, that's reasonable to save on performance). But, strictly answering the original question, yes, AI empires can trigger events.