You are much better off using the Sigma 1.4 tc with the 70-200. I have used that combo and it makes the lens a 98-280 f/4. Image quality is not affected and remains the same as without the tc and it still will still auto focus properly without any issues.
I have but will not use the Sigma 2x tc because the image quality is reduced to marginal at best for most shots, definitely softer than with the 1.4x combo.
TC's are only really good on fast primes, 2.8's for sure and a few f4's, as in 500 and 600 f4's. A lens that on the tele end is f5.6 is not to be used with a tc, not if you want any kind of quality, plus the AF will be greatly lacking. I have heard the sigma lens are much better with the Sigma tc's.