Correct, the speed of light is actually the speed of causality, we just so named it after light because that was what we first discovered as going at c, but many other things in the universe also due because it's the same underlying principle. That is why gravitational waves also travel at c, ie if you removed the sun instantaneously from the solar system, the Earth will continue to orbit for 8 minutes, as that is how long light (and the gravitational force) takes to get from the sun to the Earth.
