I suspect that an encounter close enough to a black whole to fling a star that fast would yank its planets out of orbit around it due to tidal effects.
But on the slim chance that the planets stayed around the Sun, and the radiation didn't kill us (stuff accelerating into black holes generates a ton of X-rays and so on), after the encounter itself the answer about how much it would affect us would be, "not much". The constellations in the night sky would change over time rather "quickly" as those things go, but probably not be noticeable during a human lifetime. And leaving the galaxy wouldn't cause any significant effect except for a much duller night sky, with fewer and fainter stars (and most of them would be on one "side" of the sky).
That, plus we could visit a new alien race each week as we whizzed through their regions of the universe:
And would it still be Bush's fault?
But of course.