That very well could be, when a new Pharaoh took over it's logical that he would utilize what was already there. Over time it couldn't help being chisheled away to make a new image. Some beleive that the stone was already there and cut into an image, more evidence to prove it's much older is the water marks obviously made during a much wetter time.
The Sphinx spent much of its time since the Pharoahs buried up to the neck in sand, sand filling the hollow the body was carved out of. Most of the apparent water damage is on the body, which probably means the damage or erosion happened before the end of the Pharoahs. How much before would depend on whether the body was exposed to weathering for an appreciable amount of time. If there was a wetter time perhaps there wouldn't be as much blowing sand, and the body would have stayed clear for extended times. I suspect the body of the lion was carved a really long time ago, perhaps it was the first actual major work done at the site, long before the pyramids.
How long before, who knows, but I suppose the Sphinx could have already been ancient when the big pyramids were erected; and as a special extra effect, the pyramids themselves caused the end of the wet age and the end of water erosion on the Sphinx. Don't ask me how that would work, I don't have a clue. But perhaps Great Pyramid = ecological disaster.