not if you follow the new and improved Wii softmod guide it won't.
If you just update via nintendo servers without following the softmod instructions your Wiikey will still work fine, but you may have issues loading homebrew or installing wad files (wii channels)
To correct this you would simply alter the IOS files on your wii by following the softmod guide.
If you just want to play backup discs, and dont want to play with, install, or run an homebrew, then update via nintendo and dont worry.
If you want to continue to be able to mess with homebrew, then you should follow the new and improved wii softmod guide AFTER you update via the nintendo servers.
I did this to my friends Wii and my wii and we both had a Wiikey with 1.9g
My Wii was still able to load homebrew even after update without doing the softmod guide. His was not, but after doing the guide all worked out fine.
The update did not affect our ability to load backups via the mod chip so again, if playing backups is all you want then go ahead and update.