I have a crop lens. Can I fill a full-frame sensor adding an appropriate tele converter (focal length extender? Specifically, I have a 1/2" C-mount lens and terrible vignetting on a full frame camera. I assume, adding a 2X converter will double the actual image size thus filling the bigger sensor.
Your basic assumption about teleconverters is right. But you haven't done the math:
1/2" is 6.4mm x 4.8mm—doubled is still only 12.8mm x 9.6mm.
OTOH it's not unheard-of for tiny format lenses to have image circles well larger than their specification.