Any piece of glass, not intergal to the lens, will reduce IQ. If it improved IQ, then it would be part of the lens
This and the other dogmatic replies and all those who have answered yes that IQ is always lowered by by a TC have answered a very badly phrased question and are only half right and are also half wrong. If you compare the IQ of the native lens at half the distance from the subject as the lens +2xTC, then the native lens will give better IQ since the image has the same size in both cases. But, if you compare the IQ when both native lens and the 2xTC combo at the same distance, then a good lens with a good TC will give better IQ than the native lens rezzed up. Look at comparisons on the The-digital-Picture site, for example. Of course, a bad combination could give worse results.