So I did an experiment as well. I signed out on a laptop, disconnected it from the internet and rebooted. Started lightroom - no prompts (not even one to sign in, interestingly).
I advanced the date to Dec 2019, started lightroom - no prompts, worked fine (and could get to develop). Rebooted just to see, same result (still disconnected).
I disconnected from the internet and reconnected to my network (to see if the connection itself mattered as opposed to reachability) - same result. CC desktop, if run, claimed it could not connect, but Lightroom started and ran.
I then changed to Dec 2020 and rebooted, still no connection, and now Lightroom would not run, it complained "we can't verify your subscription status" and offered me only "try again" and "quit". I could not run lightroom, no matter what I tried.
So I put the date back, put the internet back, and tried again -- same error. Turns out windows cached the connection status, and I had to do a IPCONFIG/FLUSHDNS to get Adobe back (note a reboot would have worked). Now Lightroom ran, in full feature mode. This has nothing to do with adobe I just mention it in case anyone is trying to recreate these tests on windows.
BUT... I'm still not logged in, which I think is a bit bizarre -- I just ran CC Desktop and it is at a login prompt.
Anyway... It definitely appears to me that you must, forever and ever, be able to connect to the Adobe servers in order to run Lightroom, period. If Adobe is hit by an asteroid (or an executive order, or your own country cuts off adobe's internet access) that prevents you from contacting their servers, Lightroom just does not work, in limited more or otherwise.
Thus Adobe's promise that you can access it in limited mode is dependent on internet connectivity, access to their servers, and their own continuing support of a policy of limited use, since the default in lightroom is no access at all (after being cut off for a period).