They kept things vague enough in the Superman Reborn recap, it's entirely possible to keep as much or as little as you'd like. I think a good chunk of Morrison's origin is still there, taking place immediately prior to Johns's origin, with Waid's origin mixed in there as well. Basically, any New 52 story or Pre-Flashpoint story or any other story can fit in that broad strokes history with a few tweaks here and there.
And, unless some future comic decides to contradict this belief, there's nothing standing in the way of this.