Not really. For interstellar asteroids you're looking at transit times between star systems measured in millions of years. Nuclear power isn't going to last that long. Frankly, neither is human technology. If people did somehow survive on an asteroid for millions of years, they wouldn't have any cultural memory left of how they got there or why and they would have evolved to be substantially different than humans on Earth - which they might find at their destination anyway, if Earth humans develop faster propulsion methods.