Yes, and if you have a fancy all-in-one DVR with RAID, your drive array can become corrupted if there is a power failure in the middle of a write operation.
This usually triggers a RAID consistency check when power is restored, which for a basic mirror may involve copying the entirety of one drive onto the other to fix the problem. Takes possibly days to complete with terabytes of storage.
The "well just don't let it turn off then! buy a backup generator if you have to!" argument is asinine. Controlled shutdown via UPS signalling is a normal feature of fully PC-based servers, and would be readily available if you use a PC hosted solution such as
Blue Iris.
I would be interested to nose around and see how these NVRs boot (I expect it's via a linux boot image in flash media located on the NVR motherboard), but I am not interested enough to buy NVRs just to try hacking shell access on them.