I thought Einstein suggested that gravity wasn't a wave at all, but a distortion in space-time. But my understanding of General Relativity is probably worse than yours.
General relativity does not accommodate the possibility that the sun would just disappear. The sun’s gravitational field is tied to the sun’s mass. If the sun “just disappeared” I suppose that you would have ripples in time-space and the effects would take about that long to reach earth. But remember, if the sun “just disappeared” it would take that long for it to go dark, starting at the center and propagating out to the edges. It takes light from the edge of the sun about 2.3 seconds to reach earth than light from the middle, as seen from earth.