Sharpness depends entirely on the quality of the lens and the teleconverter. But really, are you a pro shooting stuff that is going to be printed onto a gigantic advertisement outside my office? How much sharpness do you need? Will you even notice?
If you have a 50mm lens and want a 100, and a 2x teleconverter is cheaper, why not?
Honestly, I've never used one. I just have a bunch of cheap lenses, so they aren't really useful. But my camera does have a setting for 2x digital teleconverter, which is basically just cropping in-camera. Instead of using the whole sensor for 1080p video, it just samples the middle instead. You can tell it's not as good quality as without it, but it's still just fine if you really need some extra zooming.