I haven't heard this one before, but I can see the possibility. I'm not sure such pressure waves wouldn't be just as likely to suck the Earth deeper into the Sun, though. Let's face it: the Earth is pretty massive, and moving at a pretty good clip. That's a lot of momentum to overcome. And I'm not aware that they have even shown that such "pressure waves" can be produced by gravity. Not saying they can't be, but I'd like to see the explanations.
It may not be that bad, actually. I suggest you find a copy of Phil Plait's book, "Death From the Skies". He delves into all the different ways that the universe can kill us, including the Sun's expansion. But he also says that we may be able to move the Earth away into a more distant orbit, to buy us a little time. It's good reading, and not overly technical.