Well, sure, it's a sleeper ship, but who knows what they would have found on the other end? I don't think Khan had a specific destination in mind, did he?
Khan didn't design the ship; it was a pre-existing model. As Spock explained:
Captain, the DY-100 class vessel was designed for interplanetary travel only. With simple nuclear-powered engines, star travel was considered impractical at that time. It was ten thousand to one against their making it to another star system.
Khan and his followers had been beaten and were on the verge of arrest. They had to flee. They somehow obtained an existing DY-100-class vessel intended for interplanetary travel and managed to escape in it, taking a mad chance by trying to reach another star. This was a ship designed for going to Mars or the asteroids or the moons of Jupiter, most likely. There's no reason it would've been armed.
And they had
to have a specific destination in mind. Space is huge and empty. Any randomly chosen vector will probably just lead you to drift forever in the void. The only way you'd reach another star system is by setting a course for it in advance -- and even then you'd have a good chance of missing it if your calculations were off even minutely. That may well be what happened with the Botany Bay
Given their course in the direction of Menkar (Alpha Ceti, or "Ceti Alpha" as ST called it for some reason), the most likely candidates for their target star would've been Gliese 105
and Kappa Ceti
-- neither of which would be ideal choices for habitability, but they're the only nearby stars in roughly that direction, and they're at least borderline cases.