1.4x TC with a DX lens "undoes" the crop factor and lets the DX lens project an image that fills the FX frame. The angle of view is approximately preserved too, since for example 10 mm DX lens (1.5x crop factor) corresponds to a 15 mm FX lens, and the same 10 mm DX lens with a 1.4x TC becomes a 14 mm FX lens. So yes, it is doable with a Kenko or similar teleconverter, that doesn't have a protruding front element like the Nikon ones.
Is it worth doing? Hard to say. I'm sure everyone can imagine a situation when this could be useful as a stopgap. Can the 2.25 times increased pixel amount offset the aberrations caused by the teleconverter? I mean, with a D3X the options are either a 10.5 Mpix image using DX crop, or a 24 Mpix FX image with TC. There's no general rule, but my guess is that it is at best a wash and hence the use of the TC is not warranted. There probably are some lenses that make an exception and might prove to be really special.
Extension tubes with UWA lenses produce wonderful photos. The extension ring needs to be rather thin though, something like Nikon PK-11A or even thinner (Nikon K1*), but the perspective and the resulting images are spectacular. Highly recommended. If you haven't tried this, I suggest you do it asap. It is addictive!
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* Make sure you understand the limitations of K1 ring before attaching it to your gear otherwise you risk damaging something.