It might be possible to distort spacetime along your path with massive gravity spikes, not just a few waves. However, even if you did, you would have to wait a period of time proportional to the time it takes light to travel for the gravity wave/spikes to decrease the path length between you and your destiontion. Of course, the effect of trying to do so would likely disrupt the entire fabric of the universe as the equivalent of a gravity EMP propagates outward from their emitters.
I think the idea may be similar to that of The Speed of Darkness, and similar limits apply, other than the unique ability to distort spacetime. Of course, you are talking less about a nice calm ripple of gravity and more of a "Hulk is angry that the can of spam doesn't open" kind of gravity wave. Sure, the can is going to get opened, but it is less clear if any of the soft squishy meat on the inside will survive the encounter.