No it does not. A teleconverter extends the focal length of your lens, it does not make your sensor from DX to FX.
Your image sensor's size is fixed, the lens focal length is fixed (assuming a prime lens), and what the teleconverter does is make that lens 1.5 times its effective focal length. That's all.
Do you even know the difference between FX & DX?
I believe the TS knows the difference... after all, the TS is asking about mounting a DX lens onto a teleconverter, and then mounting the combination onto a camera with an FX sensor... maybe reread the TS's post?
I got a question. Let's say I was a Nikon user, and I put a 1.5X tele-converter between an old DX lens and a Full Frame sensor, would it project the image into a larger circle, effectively covering the entire full frame sensor?
well, it could work, if we can find (1) a 1.5x teleconverter that can (2) accept DX lenses... in all honesty, I have thought of this, but never got round to testing it cause don't have an FX body with me as of now...
on part (1), the common ones at the moment are 1.4x, 1.7x, 2x, and 3x teleconverters... if we go for 1.4x, it may or may not be enough of an expansion, depending on the DX lens' coverage in the first place, something that can only be tested with each particular lens... we could go for >1.5x, but the greater the value of the conversion, the greater the negative effect on the image quality, all else being equal...
regarding part (2), in the case of Nikon, please DO NOT use Nikon teleconverters on DX lenses, because most if not all DX lenses do not have the clearance in the back of the lens to accept Nikon teleconverters... if we look at Nikon teleconverters (or for that matter Canon, Sony or Sigma ones), we can see on the lens mounting side of the teleconverter there are lens elements that stick outwards, out of the teleconverter body... this sticking out portion will prevent most if not all DX lenses (and I believe even some FX lenses) from mounting onto the teleconverter... cunning, huh... please, anyone feel free to suggest DX lenses which are exceptions, cause I admittedly have not seen all DX lenses...
so for part (2), we would need a teleconverter that does not have lens elements that stick forwards... like, say, a Kenko one, where the first lens element in the "forwards" direction is recessed into the teleconverter body... that does not guarantee that the first element of the teleconverter would not hit the last portion of the lens that one would mount onto it, and I would not guarantee the safety lens-wise and/or teleconverter-wise and/or pocket-wise of any attempt to mount any lens onto such a teleconverter, so trying such a combination is strictly at your own risk... but if it does fit, it just might work... they have 1.4x, 2x, and 3x teleconverters I believe... so the most likely candidate would probably be the Kenko 1.4x...
why are there no 1.5x teleconverters specially designed to convert DX lens coverage to FX sensor coverage requirement?... so that they can sell us more lenses :bsmilie:
but do note that by adding a teleconverter, the image quality would deteriorate to some extent... obviously some lenses may work better than others, possibly the faster and better quality DX lenses, maybe say the 17-55 2.8... others lenses known for their vignetting and/or small image circles would probably struggle, like possibly the Sigma 10-20... but overall, vignetting could be quite significant still...
and also, the relative aperture value would decrease, which may mean that the camera could have a harder time autofocusing if it could actually still autofocus... and also that the exposure time would be longer, all else being equal, due to the reduction in the relative aperture value... also, the "DX lens"-"teleconverter"-"FX camera" combination would typically be longer and heavier than an equivalent "FX lens"-"FX camera" combination because of the adding the teleconverter to the setup... YMMV, and again, try at your own risk.