Does Evasion allow half damage even when unconscious?

Evasion is a class feature gained by Rogues and Monks at level 7:

At 7th level, your instinctive agility lets you dodge out of the way of certain area effects, such as a blue dragon’s lightning breath or a Fireball spell. When you are subjected to an effect that allows you to make a Dexterity saving throw to take only half damage, you instead take no damage if you succeed on the saving throw, and only half damage if you fail.

Does this feature allow a character to “dodge” area effects, taking half damage, even if they are unconscious?