#RAW - Technically, yes.
As weird as it may seem, Evasion makes you harder to hit in those circumstances. Full stop. It's because the wording of the ability doesn't give exceptions and exclusions for being unconscious, which means it allows it.

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#Rules as Interpreted
That said, a DM could justify not allowing Evasion to work when unconscious or incapacitated. Even though it should work by RAW, I'd personally advise my players I won't allow it to benefit them when they couldn't logically evade an attack simply because of the flavor associated with it.
> your instinctive agility lets you dodge out of the way of certain area effects

Logically speaking, your instincts can't help you avoid attacks if you're unconscious or otherwise incapacitated, so it doesn't make sense to still allow Evasion to save you. I wouldn't be so strict as to say they have to have movement speed, but at the very least, their instincts need to logically be able to kick in. That isn't to say how I go about it is the correct way, but a DM isn't restricted to just the RAW answer. A DM has the right to Interpret the text in order to make for a better overall experience, and this is how I choose to interpret it personally.