It might be helpful to be clear which version of the lens you're referring to: as with all lens manufacturers, Sigma seem to delight in similar namings for slight or gross variations in design.
I have the version before the 2013 "Sports" variant. That includes optical stabilisation, which I've found rather useful on some occasions - it does indeed work well on static subjects, down to implausibly slow shutter speeds.
As for the lens and the Sigma 2x DG EX TC: I'm afraid I wound up selling the TC. The 120-300 (of that generation, at least; I'm not sure if the 2013/2014 "Sports" version is optically different) certainly is good, but on the quite high resolution sensor of the D7100 (24MP APS-C), whilst I loved the concept of 600mm f/5.6, it simply didn't seem to be all that sharp when coupled with the TC. That said, that was when pixel-peeping - but then, if you're not looking at a sharp result, what's the point in the TC? By itself, the lens is satisfactorily sharp. (I say that in reference to the Nikkor 300mm f/4D, which is excellent by itself, and remains sharp with the 1.4TC. With the 1.7, I'm not so keen. Probably fine for anyone dealing in larger subjects, but I'm always having to crop)