Our power went out today, and the UPS kicked in and kept my WD NAS running just fine. I have a very minimal UPS for just the NAS for short power outages, and it can keep it running for 10-15 minutes. I am often home, and can properly turn off the NAS after five minutes or so when it appears the power is not coming right back on; and I did so today. I have never tested it in this condition to see how long it will stay on until the batteries give out.
I hope lluna is correct. but I imagine the NAS would just turn off once all power is gone. I would also think that how it shuts off is more dependent on the particular NAS and not the UPS.
There is one good way to find out, and that is to pull the plug on the UPS and wait until batteries give out and the NAS shuts down, and see how it goes. When I first connected the NAS, I did pull the plug on the UPS to see that it indeed keep the NAS running, but I also plugged the UPS back in before a minute was up. So, I never ever tested until the batteries gave out. I figured it would happen on its own sooner or later! So far, after a year and a half, no real world test of this has yet to come along.
If you do test this out fully, please report back in this thread.
I actually have a UPS to handle those momentary power blips of a second or less. Many devices cannot handle those kind of things, and a UPS eliminates problems from little pesky power blips which can wreak havoc on some gear.