Well, my caveat would be that I am using a brand-matched TC with my big zoom, so it reports corrected focal length and aperture data to the camera.
I have been using a 1.4x, because I find the hit in image quality to be too great with a 2x. That said, the shot you get is always better than the one you don't, no matter how much banging into shape you may have to do with it.
I have not found any substantial difference in shooting with the 1.4x TC on my 70-200 f/2.8 than without it, aside from having to up the shutter speed to compensate for the extra focal length. If I was shooting at a slower shutter speed, I'd use a tripod, and possibly mirror lockup, depending on the shutter speed and the shot. But these are the same rules I'd apply if I was using any lens of increased focal length, even an f/2.8 or f/4 prime.
With a 2x TC, and its two stop of light lost, I can see where you would have a much greater need for a tripod, with the slower shutter speeds. On my 10D I can just crank up the ISO, and still get pretty darned good results up to ISO 1600, so that is an option; perhaps you can find a higher ISO setting that will allow you better shutter speeds without getting too much shadow noise.