Nikon says no and I agree. First, the rear element of the 16-35mm is very exposed, and many teleconverters would hit that element. Second, teleconverters aren't very useful on anything other than telephoto lenses. Third, even putting a 1.4x teleconverter on an f/4 lens puts you in a range where autofocus performance begins to be compromised (usually only slightly, but on zoom lenses, often more than slightly). Fourth, teleconverters always rob some acuity, so you've probably already got another lens in the focal range you'd get with the teleconverter on the 16-35mm that's better. Finally, good teleconverter design takes into account the lenses it will be used on. Since Nikon's teleconverters aren't designed with anything other than the longer telephoto lenses in mind, there wouldn't be an optical match, anyway.
Oh, and one more thing: Nikon made it so you can't physically do it with their converters in the first place. You'd have to file off a tab on your teleconverter to do it. That's a pretty big warning that you shouldn’t. But third-party teleconverters may not have that tab. Be very careful about using them: you must make sure that the rear element of the lens never comes in contact with the front element of the teleconverter (that’s at all focal lengths and all focus positions).