I suspect that Khan, having been defeated twice by "regular" humans, would have taken his crew and the Reliant and used the Genesis device to terraform some nice out of the way world - probably one that had already been cataloged as boring and uninhabitable by Starfleet - with the plan of building the core of his empire there under the radar until he felt ready to at least defend it.
Then, as has been pointed out by others, there would have been no Kirk and crew to save Earth from the Whalesong probe, and, Earth being his homeworld, too, I suspect that Khan would've tried to save it, and either got killed for his trouble, or succeeded in some way (probably *not* time travel unless he managed to recover and break the security on the computer core of the Enterprise*) and then either used his position at that point to retake power at Earth, or been taken down by Starfleet.
* Although really, if you think about it, Khan and crew would probably have managed their way around mid-80s Earth a lot better. He probably wouldn't have brought whales back to the 23rd century, though. He'd probably, instead, use the tech available on the Reliant to conquer 20th century Earth, and then his empire would make sure they kept some whales alive for later.