After losing the Eugenics War, Khan and his genetically-enhanced minions flee Earth on the Botany Bay, which I guess wasn’t capable of near-light speed or even impulse since McGivers mentioned in “Space Seed” that Earth’s early interplanetary vessels were sleeper ships until the ion drive was invented for higher sublight speeds sometime in the early 21st century. So Khan and his crew couldn’t use time dilation since the Botany Boy was simply too slow.
To the contrary, I'd argue that Khan did benefit from the time dilation of high relativistic speed flight.
After all, in the episode, it is claimed that Khan slept for about two centuries. However, Khan was underway from 1996 (given in the episode) to the mid-to-late 2260s (established elsewhere in Star Trek), which amounts to 270 years, or about three centuries. How do three centuries become two? Why, because Khan is flying at an appreciable percentage of lightspeed!
In order for about 270 years of travel to become less than 250 years of cryosleep, Khan would have to be moving at about 0.45 times lightspeed. And that's in every way acceptable and desirable - because at such a speed (plus a bit of acceleration time), he would get to a distance of hundred-plus lightyears, which is great for ending up in an area of space that would be virtually unvisited for the early part of Khan's flight; then visited by humans for a while (the ENT adventures happened at such a distance); and then again abandoned by Earth traffic, like "Space Seed" says.
Also, many of the stars of the constellation Cetus are at such a distance from Earth, so Kirk could maroon Khan at the nearest habitable yet desolate planet and this would end up being Ceti Alpha V. (Or something like Eta Ceti A V, but our heroes would drop the Eta as unnecessary in the context.)
A ship capable of 0.45 times lightspeed need not be fast enough for noncryogenic interplanetary travel, mind you. It would all be a matter of acceleration. If the ship could sustain one gee, it would take about half a year to work up to said relativistic speed - and a week to go to Jupiter. But if the ship could only sustain 0.1 gee, that'd be three weeks to Jupiter, and still Khan could reach his interstellar cruising speed in a matter of just a few years. At some point, cryogenic sleep might become necessary for insystem trips, while nevertheless allowing for intersystem travel.
That is, assuming that the ship wouldn't be relying on conventional rocketry which requires propellant mass. And since the
Botany Bay doesn't look like she'd have giant fuel tanks anywhere, I guess this assumption holds true. (Yes, we can see that more than half the external containers have been jettisoned, or perhaps never bolted on in the first place - but even a full set of sixteen wouldn't give enough propellant for conventional insystem let alone interstellar rocketry. So the containers are more probably cargo, or perhaps even the location of the cryochambers.)
Timo Saloniemi