Depends on a couple of things, I believe, such as if both parties have Wii Standby Connection enabled or disabled.
As far as I recall, confirmation will happen once BOTH users have added the opposite user's Wii Address Friend Code to their systems, and BOTH have gone online.
Wii Will Rock U added my code before I added his. I added him, then forced an internet connection by going to the Wii Shop Channel (since I keep the Standby connection disabled), and upon returning to my Address Book, he was already confirmed. (I imagine he's been going online a lot throughout the day).
Right away, I sent him a message and my Mii.