Permanent connection to power is kiosk applications rarely presents a problem. Consider that your iPad will respond to background lighting levels - and will brighten the screen (and consume more power) in bright lighting conditions.
If the Power Adapter cannot provide adequate power in peak power demand, the iPad battery will deplete over time; a 5W Power Adapter is unlikely to be able to replenish the battery - leading to total depletion of the battery and eventual shut-down of the iPad. If allowed to remain in a depleted state, the iPad battery will be damaged through deep-discharge.
If you have a very old model of iPad, such as the iPad mini1, the iPad may have been supplied with a 5W Power Adapter. These devices will already have very old batteries which may themselves be on the brink of failure due their age.