Will Home Sharing work without a running iTunes instance? This is the idea: if I move my iTunes library to a NAS and enable Home Sharing, will this feature continue to work if I then turn off my PC?

I would like my Apple TV to access my music and videos but without having to keep my PC running, ideally only the NAS should be running. Is there any way this could work?
No. Home Sharing uses mDNS (Bonjour) to advertise. Without a running iTunes instance for the share, it won't be available. Your NAS may have a DNLA server built-in which could make the iTunes library on it available though.