In my experience, a teleconverter is of more use on an older camera with a "limited" number of pixels, simply because there's less opportunity for cropping or "digital zoom" from a 16m-pixel (or less) camera than there is from a 24m-pixel camera … I'm talking APS-C sensors here, you'll need to approximately double those numbers for a full-frame camera.
Obviously the lens in use needs to be of top quality. If any aberrations are visible in normal use, a teleconverter will only magnify them, and, of course, there's always the opportunity for a less-than-perfect t/c to introduce problems of it's own, including possible necessity for a different fine-tuning of the a/f
I regularly carry a 1.5x Kenko t/c, use it where necessary and often, but not always, achieve acceptable results with it. On many occasions external factors, such as heat haze, limit the range at which a photograph can be taken. Also bear in mind that unless you're starting with a fast lens, ideally f/4 or better, you'll be working at or beyond the reliable limits of the a/f system, so there can be a certain amount of unavoidable hit-or-miss in the results, even if the camera reports a "Green Hexagon".