Please clarify your question
- can you map a drive, and use a NAS, instead of local file storage, for an (almost any) app install? sure
OR
- are you asking to install and run an App (OBS in this case) on the NAS itself? if this, then, ... it depends. What OS (operating system) does your NAS run (that is for you to figure out, different NASes run different OSes). Some run proprietary/closed OS, in which case the answer is basically. no)
Most NASes aren't running Windows, so this would be the wrong forum for that question. Linux would be more likely, but even then, most likely a NAS is a bad (to terrible) fit at best. Why? real-time video encoding is computationally demanding. NASes, in general, are not designed for CPU/GPU encode heavy tasks. Are there NASes where you could do this? Yes, and they cost more than a powerful PC. so why bother?
I'd guestimate a WD NAS like you are asking about has about 1/100 (or less) of the power required to run something like OBS.
