Sigma 70 -200mm, f/2.8 w/2x Teleconverter

I am considering purchasing the above lens and dedicated teleconverter for use with my D5500. I understand that since my camera is a DX model, the lens will function like a 105 - 300mm lens on a full frame camera. If I use the teleconverter, will that make the lens function as a 210-600mm lens? Are there any issues or problems that I should anticipate if I the buy this lens & teleconverter? If instead I were to purchase the new Sigma 100-400 lens, would I be able to obtain comparable magnification at the long end?

I have that combination. It does work. Yes the 100-400mm should do the same and probably better image quality. But if memory serves me, at 400mm (using TC) you should be at F5.6 whereas with the 100-400mm you will be at F6.3 at the long end. I haven't used that lately as I have the Sigma 150-600mm C also .