Well, that sort of plays into my (admittedly far-fetched) theory over at the trailer-thread that somehow this whole movie ties into the Tarsus-massacre. I know it's not canon - but in the "Enterprise Logs" it was April in command of the Enterprise who got delayed by Klingons in bringing aid to Tarsus IV and so they arrived too late...
Of course, he can't be the captain of the Enterprise prior to Pike since the Enterprise was built later than in TOS, but he could have had command over another ship etc. And that could also explain the troubles with the Klingons... revenge against both, Klingons and Starfleet... OTOH, Cumberbatch (although he seems a bit bulkier and aged up) isn't old enough to be April - but he could still be a survivor, perhaps that guy with the eye patch that got killed by Karidian's daughter at the beginning of "The Conscience of the King".