Question about Sigma TC-2001 to 2.0x Nikon

No. Teleconverters are intended for professional lenses with continuous apertures of 2.8. and max 4.
If you need extra focal length I recommend e.g. a Tamron or Sigma 150-600mm... everything else makes no sense and is even mechanically often not possible.
If it is mechanically possible then you lose autofocus and image stabiliser.
To achieve a long focal length I recommend a DX body (1.5x crop) and a 150-600mm.
This will give you 225-900mm.

Not quite. The problem here is the lens... DX/APS_C cameras usually cannot focus at f/8 with a teleconverter. It's about the lenses... they have to have an aperture of max.4 (throughout and only with a 1.4x teleconverter) at 2.8 it's not a problem.
Teleconverters don't work with this type of zoom lens....
A 2x teleconverter would then have an aperture of 7- 12.6... with the lens.
Another reason not to buy a teleconverter is, apart from the loss of light (the light is halved -> aperture of 2.8 becomes 5.6), the image quality is reduced.
That's why I recommend a Tamron 150-600mm that costs around 950. They also have an aperture of 6.3 at 600mm.