I'm sorry, but clicking on a character does nothing other than highlight it in Easy Unicode Paster. It does not send it to the application you are in. I've tried it in several applications, and it does not work at all. It is supposed to leave the focus on the application you were in, but instead it takes the focus, which may be why it does not work.
I'm using Windows XP, and it is supposed to work in XP. Maybe it works in Vista, I don't know, but it doesn't work in XP.