I recently put my cheap (manual) 2x TC to the test. I have a DA 55-300, and took these two shots across a field. The first is at 300mm with the TC (ie 600mm), the second is 300mm without the TC and then cropped to roughly the same dimensions. Both were shot wide open (f/11.6 with the TC and f/5.8 without; my TC has an aperture lever, which works like any M or K lens, ie only wide open on my Kr).
300mm with TC 300mm cropped
As you can see, the cropped shot is much clearer and sharper. I haven't adjusted anything, just cropped. Obviously neither is a very good shot anyway, it was just a quick test. The TC shot was manually focused too, which probably didn't help. With better technique, a tripod and more post-processing you might get the TC shot a bit better, but the crop is always going to win out in equal conditions (better resolution, less light loss to compensate for). Maybe with a high quality TC on a high quality lens it might be worth it. Or if you get a 500mm mirror and want to become a private investigator
For the record, the DA 55-300 is pretty darn good. I had a Tamron 70-300 Macro, which I part-exchanged for the DA. The macro function was great, and the image quality was almost as good as the DA, but the AF was slow, noisy and hunted around a heck of a lot. Might have just been a duff copy though; my fiancee has the same lens for her Nikon and it's pretty good at AF (still a bit noisy though). The DA has Quick-Shift manual focusing too, which I love.