it is possible but it requires more then adjusting the camera. It probably requires to change every single outfit ingame and also it requires all the outfits that are modded to have a version that is compatible with this mod. The meshes basically have a separate chest part which is called by a special name. The engine recognizes this name and knows it has to erase or mask this part of the mesh in 1st person. It does this because some meshes have high collars or chest pieces that stick out these are being rendered in the 1st prsn view and basically block the view or create ugly glitches. Which means that basically all the meshes first have to be renamed, then have to be modified if necessary so that they won't glitch with the 1st person camera. Also I'm not quite sure if it will look good, there has to be a limit on how far the camera can rotate, you basically can't face your head 90 degrees down in real life as well without bending your back. Also you don't want the camera to rotate through the body and show the inside of the mesh so there have to be certain limits. [Though this is based on my knowledge of this for oblivion, fo3 and fnv and assuming that it works the same for skyrim]
Appreciate the reply. I see what you're saying, in Skyrim and other first-person games, your head just kind of "pans" from a central location. This wouldn't work with a first-person body, because you'd be able to see into your chest. In real life, your head actually bends forward when looking 90 degrees down.
Not sure what would be the best fix... trying to simulate real life may make the controls feel awkward, and limiting how far you can look down is... limiting.