No, I'm not sure about it. And general relativity did predict gravity waves, and did generally describe gravity as being the curvature of spacetime.

Having said that, if "gravity waves" move at the speed of light, but speed is distance over time, how can you measure a "speed" when the thing whose speed you're measuring warps the units you use to measure it? It seems like you could talk about the movement of gravitational waves from the point of view of an observer outside the system with a ruler and a stopwatch that were unaffected by gravity. But, general relativity seems to suggest that there are no absolute / external reference frames you could use.

I fully admit that I don't completely get general relativity, and that it has been a very useful model. It just seems like it can be a useful model even if there are certain dusty corners where you shouldn't spend too much time looking because things stop making sense there.