Yes, you get all the data. Sometimes you can see even more than what the Wii shows you. For example, with the Wiimotes, it actually shows you the position and brightness of the top 3 or 4 infrared light sources in its field of view (from that it can derive the position of the "sensor" bar).
If you have a link, it would be much appreciated. When I looked I didn’t see anything that came close to the functionality that the Balance Board had when attached to the Wii. It’s nice that the raw data is available, but unless it’s presented in a way that’s useful, it’s not that interesting.
The only project I found was FitScales and it has been dead for a long time now because Android Bluetooth changes made it incompatible with newer devices.