For some background:
The reason you typically get a NAS appliance is to get something that will serve up storage and "just work". Of course you need to do an initial configuration, but after that, you pretty much just leave it alone until a drive fails, or there's a critical firmware update. For a Windows file server, you'll need to do regular maintenance (patching, etc).
NAS devices can also offer excellent performance, and nice features like hot-swap/hot-add of drives. They also will handle building your RAID volumes for you with minor effort on your part.
You can join most NAS's to corporate domains, so additional authentication is not an issue.
For your particular scenario:
If you already own the Windows file server (hardware and licensing), then you're pretty much good to go. It should work OK for your needs and there's no reason to replace it with a NAS. My only question would be, does it at least have a RAID1 for the storage drive? I would recommend that in addition to backups ... it will save you trouble in the long run.
HOWEVER - If you don't already own the server, than it is worth looking at SMB level NAS units. You can get a good quality 4-disk NAS for MUCH cheaper than a new server+licensing. ($1000 or so). The only main question here would be if your particular backup solution will work OK if backing up off a remote target (you won't be able to install a backup client directly on the NAS).
You mentioned FreeNAS - that and Openfiler are viable options for your scenario. I have built an Openfiler box used for a similar scenario as yours and it works well. I was able to join it to an AD-based domain and it works fine. If you are comfortable building a rig from scratch this method would be cheap and effective, but keep in mind you're on the hook for hardware repairs.
NAS=Windows Sharebe careful throwing that equality around. The 2 terms are more like a Venn Diagram with overlapping parts rather than equal.