Eh, both permanent space habitation as well as generation ships are so comically far out of our reach that any effort to escape would be doomed. All the billionaires would have accomplished is that they'd die slower. Unless we had decades of advanced warning and even then it would be a stretch. Additionally, in the latter case there's no need to keep it secret. The world is going to end in 50 years just wouldn't cause as much panic.

Secondly, if you look at the picture, the projectile directly pierces the earth. So it would have to be going extremely fast to accomplish this. So chances are we wouldn't see it coming to begin with.

Thirdly, this sort of direct hit implies intelligence. So, chances are whatever wants us dead would then follow through to ensure they get any survivors. Or not, as I pointed out earlier, all survivors are screwed either way.