no you would type wXXXXXXXXXXXXXXXX@wii.com, then you send the mail. and yeah it does take a while sometimes to get from your computer to your wii.
obviously replace the "x"s with your wii's number.
also i forgot to mention. you have to "register" that email on your wii, you go to your message board, click "add contact" or "add email" (if there isn't an "add email" just use the "add contact" and type an email instead of a wii number.)i forget and i'm not home right now, then type your email and name and it'll email you directions on how to email a wii.
if you still need help later i'll be happy to when i get home.