I have a B+ setup as network storage at home. It works superbly well for me, and I have no doubt a zero would work equally well, but you have to consider your use case a bit.
Using a zero for a NAS would mean that your HDD needs an external power source (if I'm mistaken on this I assume someone will correct me), and you need a Ethernet/USB converter. The zero has limited computing power and isn't likely to handle any type of heavy applications very well, so auto-syncing via OwnCloud WebDAV may be taxing, depending on the rate and size of file system changes on the client. Also remember that the ethernet and HDD will share the USB bus to the processor, so whenever a file is transferred over the network it has to travel through that bottleneck twice, effectively cutting the transfer speed to half of what the USB bus can deliver. If more than one client uses it simultaneously this is likely to make a pretty big difference.
My "NAS" handles small files and does no auto-syncing at all. 99% of the time it just idles, and then every now and again I rsync some files to/from it. I rarely handle any large files, but when I've done so it's been obvious how slow it is.
What do you want your NAS to accomplish?