I can tell you EXACTLY what they do. They are termed Splash Rails, and when rocking side to side in a chop, they keep some of the splashing out of the cockpit. BUT, that is not actually their purpose. If you look at any Hatteras, there is very little hull flare toward the stern (the rub rail doesn't stick out far past the hull). These spray rails protect the hull from rocking back and forth in the slip from the hull itself hitting the pilings/dock.
Original ones on early models like my '69 45C were made of solid mahogany with a solid SS rubrail on the outer edge. The new ones are molded fiberglass, with the SS rubrail. DON'T remove them, as you risk hull damage in a storm. Take a look at some of the large (53' and up) older Hatts and you'll notice quite a few of them have damaged splash rails from hitting pilings and the like.
Other boats with these will be the Carolina style boats such as Davis Yachts, Rybovich, etc. On some of these boats, the hull actually bulges out up to a foot farther out than the rubrail!!!
FWIW, Tom Slane has the mold to recreate the splash rails for most of the old Hatts. Mine were damaged in '04 storms, and I had Tom make me a pair. I had a great experience with Slane Marine...if anyone wants to know more, let me know.
Look how the rubrail on this boat (Buddy Davis) would do nothing for the aft section of the boat in a slip. This is the same for our boats, only to a lesser degree.
Jason