There is no reason why Khan can't be in STID. When the Klingons had the Narada, they could easily read the Narada history files, notice the story about Khan, look for his ship, brought him and his crew back to Qo'noS.
Once they have gotten him there. They would had woke him and his crew up.
The question would be. Is Harrison Klan, or is he and Khan two separate person? Most likely that Harrison and Khan are the same person, but two different people.