I’m in the middle of moving house and have my priorities sorted (I upgraded to Papyrus Author+), but we are going to be without internet for a couple of weeks.
Will the software work ok without being connected?
Congrats–Here’s wishing you a hassle-free move! 
Papyrus Author runs without an active internet connection, but it needs an occasional online check-in for authentication and updates.
If you’re away from your internet connection for a longer period, you can briefly share your phone’s connection if needed. The check-in takes just a few seconds, and after that it works offline for a good while again.
Does your cell phone and plan support tethering? I often use this and a cloud service to move my current project between my laptop and my desktop if I forget or can’t move it manually before work.
As for the root of your question, yes. It will not bother you for about two weeks in offline mode; but after 14 days (I think) it’ll start saying nope! Gotta check you’ve paid up!
I think it does this so people can’t pay the sub once and then gleefully cancel their sub and keep writing forever just by isolating their device from the internet. xD