I was about to file a support ticket, until I found this. Yep, it does seem to be a bug with Nova Launcher, as after posting this to Evernote's support Twitter page, I tested it with the stock Samsung launcher, and Nova on my tablet (after rooting it, its stock Lenovo launcher kept crashing, and by the way, they suck at updating their Androids), and found what it really was,
Yep! This feature would really come in handy as I have my old notes from my school days that I don't want to lose, among other things. I imagine that, by default, notes in Archive and Trash wouldn't be saved for offline viewing and editing, but the rest would be.