McCoy, judging by his backstory about his divorce and joining Starfleet seems to pan out across both universes, and doesn't seem like the difference in the timeline would effect that much in 2255.
Except that they're not writing this show with any interest in being consistent with Abrams. McCoy has no established, consistent backstory. They just told a version that suited them in Star Trek 2009. The SNW people have no reason to refer to that backstory at all.
They did go out of their way to separate SNW Kirk's life from Kelvin Kirk's, in just about every way they could. And what we know about Lieutenant J.G. Scott's situation has nothing to do with the Kelvin version at all.