You are correct. Thanks for pointing that out; I tested it out this morning and verified I was able to send/receive messages on the desktop program with my phone in airplane mode.
With the rapid churn of various chat clients it's hard to get something to stick, and I attempted to settle on XMPP+OMEMO (or OTR), since it's a protocol, not an "app" (eww). Not a single person I know still uses XMPP, and it's easier to just tell people "Download Signal". However, that requires a phone number, and is useless on a desktop if your phone's off. Despite being Free Software, it's fairly locked down.
Secure communication with most people is nigh impossible these days, because nobody wants to not use SMS.
There has to be a better solution, and despite email+PGP's flaws, it's the only system I've seen that's stood the test of time. There are pretty good plugins for Mail.app (macOS) and Outlook (Windows), and if you use Linux you probably can deal with gpg. We use it at work for email, and pretty much everyone can work with it at any level of technical expertise. Anyone else have any solutions that have worked in their circles, including non-technical family members?