A reputable poster on the MacRumors forum has made a post stating the Nintendo Wii online beta test is running from September 18 until October 23rd, 2006.
He says the tests will cover the Wii Connect 24, the Virtual Console and other online features.When I beta tested the DS wifi we did that for almost three months until Nintendo Wi Fi was launched but that covered three different games. I guess the system could launch but then the above features won't be up and running if it did. So hope that helps in narrowing down the date.
Didnt want to post this in the news forum as its purely speculation right now, but the poster in questions has a good reputation for Nintendo related news.
You can read the thread here: http://forums.macrumors.com/showthread.php?t=232772