We at the blog love to demonstrate new, cutting edge features and documenting them for current and future users of the emulator. Wii USB device emulation is one of those things that lacks data and testing in Dolphin. It requires real hardware just to try it out and only a select few people are crazy enough to work on anything involving the Wii IOS HLE. The first time E-ticket Service Launch support was added to Dolphin, it managed to break connecting Wiimotes; that's just how touchy that code can be!
When looking around, the most common answer is that USB Devices won't work with Dolphin, with examples of the Konami microphones being given and recommendations toward an old branch that implemented Wii Speak support (which still doesn't support those microphones.) For anyone searching, the answer to "Do Wii USB devices work in Dolphin?" came up as a flat no on the wiki, issue tracker, and forums.
It turns out that a lot of these devices work perfectly in Dolphin! Support was added way back in 2013, but seems to have been mostly forgotten by time. The primary reason for this was that it was a part of the Wii Networking merge. The main focus of that merge was to add Wifi support to Dolphin for playing games on the still active Nintendo servers. Hidden within that was an USB HID implementation for Dolphin. Somehow, this wasn't really tested or noted for the most part and snuck into the emulator almost unnoticed. When a discussion about this came up on IRC a few days ago, we just had to try and see what would happen when we plugged some Wii accessories into our computers for Dolphin.