It will not be used as much as the nunchuck, classic controller, or Zapper by my prediction.
But I do believe it will be used more than the DK Bongos. The bongos were a specialized product from the start, with the barrel design and DK logo. On the other hand, the Wii Balance Board is just another accessory. As far as I know, it doesn't have any WiiFit-specific markings.
Also the bongos were more limiting in their abilities: two large buttons, one start button, and a clap sensor. The balance board alone has but two pressure-sensitive buttons, but can be used with the remote (although it could get a little difficult).