Quinoa smoothies really do exist -- the Cooking Quinoa website has 2 recipes, using either quinoa flakes or flour, but I see no reason not to use cooked quinoa too.
http://www.cookingquinoa.net/smoothie-recipes (with a link to another recipe)

Cooked quinoa would probably work, but may not blend in totally smoothly. Would be worth giving it a go, though.