When you enchant a 'Carrot on a Stick' or a fishing rod on the enchantment table, it will give you nothing and Unbreaking 1 enchantment on each level.

Survival
In survival mode, the selection button is greyed out and cannot tap the button, when selected it will send a message: "No valid output for this item".

Creative
Can tap the button, the button isn't greyed out and not applying any enchantment when selected, but it doesn't cost any XP or lapis.