1. There are no automatic updates on the Wii whatsoever.
2. Updates do not affect BootMii as boot2 (unless boot2 is updated).
If you are on 4.2 or 4.3 System Menu you should already have the newest boot2 and the update will not affect it. If you are lower than 4.2 you can update with the game but BootMii will be removed. You can re-install BootMii after the update and it will work as it does now.
So, in short, if you are lower than 4.2 you should make sure you have the latest Homebrew Channel (1.0.8) and then update the Wii using either your game disc or the online update which can be found in the Wii Settings. After this you should install BootMii as boot2 again (the latest version as well).
If you are on 4.2 or 4.3 then just update as I said before and you will not have to worry about BootMii being removed or bricking your Wii.