Feels like a stupid question, but I’m moving home on Monday & have a long drive ahead. I’ve downloaded a bunch of albums to my phone but everything else will be packed away.
Now, I get that the music is on my phone, but with past ARC problems, “pinging the server” has been mentioned.
At the time I took this to mean the Roon servers & not my core, but I wanted to check, because all my gear will be dismantled & in the back of a van.
Theoretically I think it should. But I’ve had issues before. I’m trying it now since the new update (since my Arc can’t work normally as it is). My advice is also have a streaming service you can access.
Shut down your Roon server and phone WIFI and try it.
It plays downloaded files if you have no phone network and can’t reach the RoonServer, so surely it can do the same if it can’t reach your server for other reasons - if you have no phone network, it can’t even know if the server is running.
For how long, I don’t known
Never had it reliably work well in offline mode which is essentially the same thing. Tried it away from home in offline mode a number of times and It did work for a while then stopped and it refused to access any downloaded material on the device until it could connect to my server. This was only a weekend so not a great length of time. YMMV.
I run mine in offline mode a lot and the latter builds work fine, for me, for a week or more.
When I replaced my Roon server recently I downloaded a whole load of albums in ARC and put it into offline mode.
It worked perfectly for me for about a week until I was ready to put the new server live.
I am guessing that if you also put it offline before the disconnection that you would also have the same experience.
Good luck 
Thanks for all the replies. It does indeed work perfectly well.