It depends what type of website you're planning to host. If it's just some static files, then it should work. However, I think you'll find that the webserver built into the NAS doesn't support a lot of the functionality required for dynamic websites (eg PHP, MySQL/PDO libraries etc). Even if you got lucky and found the NAS does support that, you'd still have to have somewhere to host a MySQL server itself and I doubt the NAS would do that.
Makes sense whenm I think about it now. For the cost of a NAS I could do also a small linux box (on obsolete hardware) with CentOS (or whatever) and have a fully expandle server where I can upgrade the hardware every time a need it.
Plus, my NAS is a filestore, I like to keep that data safe.