While trying to answer this question I ran into a strange behavior.
checkout_cart_add_product_complete event is working nice while adding a product to cart from a catalog. However if I try to move product to cart from a wishlist the event doesn't fire.
The reason for it
Mage_Wishlist_IndexController::cartAction() is adding product to cart through
Mage_Checkout_Model_Cart::addProduct() method and not through cart controller (where
checkout_cart_add_product_complete is firing).
So the question is if it was made intentionally or is it a bug?