Mm, people over at the Wiird forums say you should never update from a disc, but to update by launching through Gecko instead. Gecko just installs the IOS's straight from the disc, while updating through the disc menu messes with your firmware (I think
).
And no exploit requires any Internet access.
As for how LetterBomb works, well I haven't really looked much into it, but I'm sure you've heard of BannerBomb. It uses a (purposely) badly designed channel banner to run unauthorized code (in this case, your homebrew). LetterBomb does something similar, except that it runs the exploit from reading a specified letter in your Wii mailbox (or whatever it's called).