Most off the shelf NAS will not run sabnzbd as they run their own proprietry operating system. What you need is something like the Microserver where you can install Windows or Linux and then any apps you need.
There are a number of pre-built NAS such as the Buffalo Linkstations where you can wipe the installed OS and install a fully functional Linux distribution though this is not for the faint-hearted and will most likely void your warranty.
Scratch that, sabnzbd can be run on a handful of NAS devices but they're not officially supported and a few hacks are required. There's a link to tutorials from their site: Install on NAS devices - SABnzbd