It won't work through a dongle. The dongle only tells the card to output component into VGA, the gun would have no idea what to do with the video going through it, and attempts to make the screen flash would cause weird troubles. Possibily even damage could be cuased.
However, there are converters that take VGA and transcode it to component, I don't see any problems connecting one of these after the VGA lightgun and using it on an HDTV.
One more possibilty, many TVs can switch between component and S-video, if you get a card that can output both S-Video and Componet, you just use the TV gun on the S-Video, and switch to component when you're not using the gun for better quality.