There are various kinds of disables in League of Legends. These include stuns, suppression, silences, slows, fear, and more. Each one can be equally frustrating if you get caught in them and equally fun if you manage to get your enemies caught in them.
League of Legends has a knack for a very smooth learning curve for new players but has layers of depth in the game that pro-players are still discovering, exploring, and talking about. New players find it easy to learn League of Legends, whereas pro players have lots of opportunities to explore new mechanics in the game.
Some players have alleged that smite can be used while being stunned. Similarly, others have argued that summoner spells can be used while being stunned; the logic there is that stuns work on the champion but not on the summoner or player (YOU!), so summoner spells are safe to use while being stunned. Another debate that can be found on Reddit and other chat forums is whether or not you can use smite while under the effect of Zhonya’s active.
Then again, the summoner spell that is possible to be used under a stun actually varies from spell to spell. The same is true for all the different kinds of disables i.e. the summoner spell that can be cast while under the effect of a particular disable depends on the disabling effect as well as the summoner spell.
There could be an entire article about how to get free from different kinds of stuns. For example, Silence stops Flash and Teleport but not others. As far as the possibility of using Smite while being stunned is concerned, you can try it for yourself. Many users have said that it’s entirely possible to use smite while under the effect of stun. The only disabling effect that can stop you from casting Smite is “Suppression”.
But such is the beauty of League of Legends. There are so many layers to this game that it’s safe to say they have not yet been explored entirely. As the game develops from season to season, new game mechanics are evolving, and there is more and more to explore in League.