Yes, how it came to pass means how it happened.

I think there is a slight difference. When you say "Thats how it came to pass" it means that eventually after some time or certain process these was an outcome. There was time in between the event, sort of insinuating that it took steps to get there or a progression- one event led to another to get to the end point. Vs "Thats how it happened" which could be something that is less on the side of a series of events that may not be well related but more of a recounting of events.