I have used it with and with out and am unsure if I remember seeing a difference. I may do an experiment on my days off to see if there is a difference.
You'll probably get to this before I will, but could you post your findings? The amount of sun we have here is similar to Alice, but a lot more intense. I typically need a hood on all my lenses, but I'm not so sure about the so-called hood for the 16-35.