It depends on the NAS system.
Some people take a Linux server, add tons of hard drives, install a specific distro and call their server a NAS. Those types of machines could probably run Intersect via mono, a MySQL database, and anything else you might need.
If you get a NAS device that’s only capable of the basic file storage/retrieval with a proprietary os in which you don’t have a shell and can’t run your own software than you’d be out of luck.
Furthermore, in my limited experience NAS systems have a good network connection and lots of storage space but generally have low end/slow processors. For most games this won’t be a problem but if you’re aiming to have a professional game with lots of players online then you’ll ultimately want a server with a really good processor. (The amount of storage won’t really matter for an Intersect game.)
As @SkywardRiver and @panda have already mentioned VPSs are generally the way to go for these sorts of games. That being said, if you provide the specs to the NAS you’re looking into we might be able to give you a much better response.