On an f/4 lens the 2x will push the minimum requirements. The D750 should be able to AF up to f/8 which is where you're at with a 2x. If light is low it might start hunting and you'll probably require f/11 to get sharp shots.
If the 2x will outperform crop is something you have to find out. The quality will go down quite a bit when using a 2x. If the 200mm shot is sharp, I'd bet crop could outperform the 2x, if done correctly.
I don't know your lens but when I shoot my 70-200mm f/2.8, and I take a good shot, I can easily crop that until 100%.
If you have the Nikon 70-200 f/4; I just checked the sharpness. It's sharpest at f/5.6 @200mm and degrades a bit at f/11 but not that much. Still, if you connected a 2x between, that sharpness will go down quite some more. I'd test if cropping works well and how far you can take it. You lens should easily be able to take perfectly sharp shots at 200mm, even when zoomed in fully at those shots.
I'd rather use a 1.4x on that lens. 200mm is indeed short but the Nikon 2x costs around 500$ I think. The 1.4x too if I remember well. That's about 1/3th the price of a 300mm f/4 prime.
Many of us first try some alternative approach; be it extension rings, TCs or diopters but in the end, most of us end up buying that lens anyways.
