They'll be happy to contract with a salvor - no guaranteed pay, of course, but they'll be pleased to take a huge hunk.
The Law of the Sea is of interest inasmuch as it shows how the Law of Outer Space, Space Law, will develop. There is the 200-mile limit, the continental shelf, and the deep sea, the legal situation covered by various issues of sovereignty and international treaty. For outer space, a region of the law that is rapidly becoming more interesting, there is the 1967 UN Treaty on Outer Space and a few other treaties, and then the rest is extensions of the Law of the Sea.
Major developments are on the way depending on how rapidly ownership of space resources is asserted. The moon will be first, and is already being claimed in part. For example, Tranquillity Base, the site of the first Apollo landing is already designated a National Park or Historical Place, something like that, under jurisdiction of a Federal agency, Park Service or Forest Service, I forget which. In any case, there won't be any salvage operations by private adventurers of the equipment that Armstrong and Aldrin left on the moon.