Pretty sure that, even if we managed to haul every piece of the moon back to Earth, we would not get close to the material required to fill the circled area. It'd be sufficient for maybe 5 miles of extending the coast line, but not much more.
I went a more math-less way when I read this originally. The moon is about a quarter the width (diameter) of the Earth, and the variances in the height of the Earth's crust (mountains and trenches) aren't visible in satellite images of Earth. If you cut the moon in half and put it down in the Atlantic, would it change the contour of the Earth's crust as seen from orbit? Yeah, it'd be another eighth-again as wide on one side. You'd notice.
Doing some quick checking confirms: the Atlantic has a volume of about 355 million cubic kilometers. The moon is about 22 billion cubic kilometers. So you'd only need about 1.6% of the moon to fill up the Atlantic.