Ok, here's the end all, be all confirmation...
WiiSpeak in Animal Crossing works with any generic mic (I have the Logitech USB mic which also works with Guitar Hero, Boogie, Rock Band, and the Disney singing games)
WiiSpeak CHANNEL only works with the WiiSpeak OFFICIAL accessory.
I am on Wii System 3.2U with Starfall installed.
If you are on any Wii System lower than 3.4, you need to install IOS55 and the Animal Crossing fix (I believe it's IOS51), and IOS38. That will allow you to use the OFFICIAL WiiSpeak Channel and OFFICIAL WiiSpeak mic accessory.
So far (at the time of this post), you can ONLY use the OFFICIAL WiiSpeak accessory mic to access the WiiSpeak channel. If you don't have the OFFICIAL WiiSpeak accessory mic, it will tell you to turn off your Wii, and reconnect it before starting the channel again.