Nope, it's a completely physical process and state, so you can disconnect it and the image will remain the same. So you could use it as a reusable post card if you wanted, but for $80 maybe it's not such a good idea...
I don't really know why they recommend to clear the screen after leaving the same image in for 24 hours, but I think it's mostly a precaution and most likely not a real issue. But for my own sanity, I do clear it at 2am and then it's already drawn a new image at 8am, before I'm out of bed.
I had some “burn-in” on a 4 in waveshare display that lasted for about 10 refreshes. I bought it used so who knows how long it was stuck on that one screen
I don't really know why they recommend to clear the screen after leaving the same image in for 24 hours, but I think it's mostly a precaution and most likely not a real issue. But for my own sanity, I do clear it at 2am and then it's already drawn a new image at 8am, before I'm out of bed.