For the saiyan race to be re-purified (i.e., the human blood erradicated), there would have to be a lot of inbreeding. So aside from the whole "thrown to the future" thing, I think they're pretty screwed. Unless Pan went back to the past as an adult and got impregnated by a full blooded saiyan and then came back to the future. That could work. But that's messy and we have a Futurama "own grandpa" scenario. As for your story, I like it.

Hey, how many saiyans does it take to screw in a lightbulb?

One, but it takes 8 episodes.