I know there are issues with up and moving the entire iTunes folder, something to do with the way iTunes knows where the music files are I think. Personally I'd just COPY the actual music files over to the NAS and set up a new library from scratch.
If you think of it as starting from scratch with iTunes. You'll have all your music files in a folder on the NAS, you can call the folder anything you like. When you start iTunes holding the shift key and create a new library it puts a folder on the NAS that holds the library file and other associated files. You'll then have a blank library showing which you can add the folders on the NAS to. iTunes will add the artwork from scratch (you can manually do the ones it misses)
iTunes will then open to this library unless you tell it otherwise (by the shift key on opening) So it should add new stuff to that folder as it would if it were on your PC. There is a flaw in the plan, as there always is, if the NAS is unreachable for any reason when you start iTunes it will create a new blank library on your PC and you'll need to reselect the NAS library.