We are all accidents. Most people's parents met as a result of chance events. This poses no problem for Catholic theology, for we hold that nothing is random for God. He sees all and knows all. Thus what appears to be an accident to us is not an accident to God.
it was not an accident, and it was part of God's plan, his planned end game, than you are positing mechanisms that inevitably lead to the emergence of homo sapiens, and that gets rather near to ID, does it not?
No. ID posits that natural processes are insufficient to explain the diversity of life on Earth. The Catholic view of evolution does not make any such assertion. It merely asserts that everything that happens on Earth, even random events and accidents, are part of God's plan, for He is outside time and knows all.
No, I doubt that happened personally, but that is just my Baysian take on matters.
Besides, "random" really means "random to our puny minds."