Yeah, it'll work plugged in. Since the dashboard mode locks everything down until restart, you can leave it connected. Though keeping it constantly charging might turn your battery into a spicy pillow eventually - maybe chuck it on a smart plug to charge for an hour every few days if you're worried about that.
Even better if you can get the kindle to control the smart plug and therefore the charge cycle. Keep the battery in a non-stressing range of 40-60% or something like that.