IF there is any Khan connection it could be that “John Harrison” is actually Khan using an alias or it could be that John Harrison is his real name and he is one of the other genetically modified supermen from the botany bay.
May be Khan’s empire was India/Asia/Middle East and John Harrison controlled the UK/Europe during the eugenics war? Harrison hitched a ride with Khan?
One of the articles at trekmovie mentioned that trailer 2 has a shot of a “large room (possibly shuttle bay or cargo hold) filled with tubes which have small windows (or possibly control panels) on the top”. Without seeing the trailer it’s hard to say how big these tubes are, but if they’re big enough to fit people in it could be that someone has multiple augments from the botany bay still cryogenically frozen in their possession.
You, sir or ma'am, may have something there. This story is obviously, with the inclusion of Carol Marcus, taking place in the "Khan mileau", and it appears 'Batch's character has some super-human ability. So it may be another of the genetic supermen back to wreak havoc, maybe to avenge Khan's death at the hands of the Klingons? And the Harrison name may just be a coincidence as far as the TOS background character goes.