The Mythbusters did that already, in Episode 76 (http://mythbustersresults.com/episode76). So we know that works already...

But ... but my dominant hand keeps taking the mouse back again!

Unless the math is wrong, or a solar storm changes the track or ... and you alter the path to make it hit dead center instead of a grazing shot. That's the problem with orbital mechanics - stuff changes over the years and depending on other gravitational interactions, what you thought was a deflection was a centering action. W00t.

But you *know* there's a rock out there with Humanity's name on it. This one. Another one. Doesn't really matter. If we can't get off this planet in serious numbers before it hits, the universe goes on without us.