There are a few aspects to this question.
Physical connection: will they mate up and connect to the camera and operate? Almost definitely, sometimes with some limitations (and occasionally with some extras: the Kenko teleconverters connect in with Canon lenses and allow them to autofocus at F8 instead of F5.6, although I found the actual use in the field too unreliable to depend on. It did work).
Image quality: Vendor TCs are generally designed to work with specific lenses. The Canon TCs aren't supported for use on all Canon lenses and may not give quality results with unsupported lenses; many of the unsupported lenses for teleconverters are the zooms. You'll get loss of sharpness and contrast to varying degrees and in some cases some rather nasty chromatic aberration effects or corner warping.
The only real way to know for a specific combination of teleconverter and lens is to try it. Find a buddy with the piece you need, or rent it from a place like borrowlenses or lensrentals and go out in the field and take test shots. Then load them up and pixelpeep away to see if you think the quality is acceptable for your needs. There's no "vendor support page" or "in theory" answer that'll get you a definitive result here, ultimately it's going to require a field test.
The Canon 2X III TC is an incredibly sharp unit, FWIW. And it works very well on high end Canon zooms. That sigma lens is supposed to be good, so I think the combo has potential, but I haven't tried it. it'd be a worthwhile test, though.
The new Tamron 150-600 looks really interesting to me as a bird photographer. I've arranged a test unit that I expect to put through its paces and write up in February. At that price, I think it'll blow the Sigma 150-500 away in the market and I'm tempted to buy a unit myself. We'll see how it works in real life. I would not expect good results for the 2X TC attached to that lens, though. I'll probably test it to see, but I wouldn't expect to use that combo out in the field.