If you are asking about running Rock Band from a disc without any IOS hacks involved, it should work out-of-the-box.
If you are asking if IOS222 works on vWii, I'm not entirely sure. Though, I have found one piece of info online that states:

d2x (IOS249, 250 and 251) is officially supported on vWii, to try using this first. See the Definitive vWii hacking guide for more info.

 

To do that, you will need to install the d2x IOS.
The Definitive Guide mentioned above recommends USB Loader GX (in conjunction with Nintendon't for GameCube Games.)

Just a note that the Wii U will attempt to format your drive if you connect it to the console while in Wii U mode. A tool called UStealth hides it from the Wii U, but not from compatible vWii software, such as USB Loader GX.

If you need any help with vWii, most answers will likely be in that definitive guide, but don't be afraid to ask (as long as you ask valid questions, and don't troll).

 

Rhythm games were my life for like 5 years lol. I feel your pain on the original Wii, getting them to work was beyond painful. If you follow my guide, as I assume you did, you will find (as you have) that the games function perfectly! If you have a USB Hub, you can even use the back USB ports for instruments that require them, like some of the drum sets, RB Guitars, and the mics. I'd still recommend trying to get your hands on the GH3 and GH:WT guitars as they just plug into the Wii Mote. Some of the RB drums use the Wii Mote rather than a dongle, as well as most Guitar Hero drumsets. This way you can avoid as much clutter near the back of your Wii U as possible.