I don't think that John is Khan either.
If Khan is in the film, he'll have a very small role, guiding the events that are happening
My theory is John found Khan and the Botany Bay instead of Kirk, and he agrees with Khan's ideals and is working with him (or for him).
Also remember John is starfleet, he could get into places, do things that Khan would not be able too.
John also appears to have super strength, fighting off many Klingons at once according to the trailer, so he maybe some sort of Khan analogue, based on a canon character, but not that character exactly.