Well, if it's possible, the Oracle is in the best position to do it. The Oracle is designed to study the human psyche. With the Architect they are creators of the current Matrix version.
Presumably the Oracle can access data on the very minds of the full lifetime of each and every person from lots of generations of full human populations.
Combined with the understanding of human psyche, and adding that machines probably supply the humans with the building blocks of each Zion, and that the starting population of Zion is selected under the control of the Machines, and 'the vase', I would say, yes, the Oracle can predict these 'accidents'.
I'd add that maybe it's the Tank-specific part of subconscious of Cypher that makes him miss Tank under psychical stress, the Vigilant's demise is the workings of Smith who is a program, like Squids.