I guess it is possible but very inconvenient. From my understanding you have to save edits to Apple‘s Camera Roll which you could then export to a NAS. I still cannot understand, why Adobe does not offer a decent NAS integration with any of the wellknown brands. This could solve so many problems as for instance backups, slow sync between Lightroom mobile and Lightroom classic, Library access from Smart TVs etc..
Assuming, I am not the only monthly paying customer with this feature request I would like to know, why there is indecent NAS integration?
I would assume it's because Adobe wants to push their own cloud service and have people pay for upgraded storage. I'm afraid it's as simple as that.
I recently got an iPad Pro and a home Cloud NAS; I've been working with the LR library on dropbox and all data on external hard drives to almost seamlessly being able to switch working on iMac, Macbook, ... My dream is that I could store all my data on my NAS (because we're talking terra-bytes of data, here - nothing I want to store locally on my iPad, for example, because it will eat up the internal storage SO fast) and only sync the library through Adobe CC, accessing the photos on the NAS from all devices, including remotely. Unfortunately I guess that will remain a dream, at least for now. At this point, for me Lightroom mobile is pretty pointless other than for the occasional snapshot the way it is.
I sometimes feel some of the implementations are just not with the professional user in mind. The hobby photographer, who takes a couple of pictures here and a few pictures there is probably perfectly fine with the Adobe Cloud, but anyone who does photography semi-professionally or professionally comes back with hundreds and thousands of pictures per shooting.
I agree that Adobe would want push customers in the direction of their Cloud services, but I don’t think it’s as simple as that.
One of the ideas of Lightroom CC is that it reduces the issues that the less experienced users of Lightroom Classic face (missing photos & conflicts, wrong catalog etc.). I very much doubt that they would want to revisit this with offline uncontrolled storage in a Mobile environment.