Yes, at the widest settings in particular.
Using a fixed 24mm lens (on a full frame camera, which is the equivalent of your 16mm) I sometimes get wildly variable darkening over the width of the sky. It can look okay in a single image, sometimes. But I would hate to have to stitch a panoramic with a polarizer.
The polarizer effect is variable and depends on a lot of things, but you'll want to experiment before using it. That's not to say you shouldn't have one for this lens -- it's very useful for single images.