The updates are indeed for the online aspects of the Wii. If you have a home wireless network, then you will probably want to perform the updates NOW, rather than wait for Christmas morning. First, because there will be a huge amount of traffic to the Nintendo site as 100,000's of Wiis connect for the first time and attempt to download the update. Another reason for doing the updates now is to get it out of the way so that you can spend Christmas day playing games and making Miis. (I'm sure the kids will have friends who also have or will get a Wii on Christmas and they'll want to exchange Miis with each other). And lastly, if you wait until Christmas to perform the updates and by rare chance the update fails and bricks the Wii, it will be out of commission on Christmas day.
Doing the updates now gives you time to get a replacement from Nintendo IF (a very slight possibility) it bricks.
Considering the number of consoles sold, reports of problems is extremely low.
If you don't plan on going online EVER, then don't worry about the updates.