Logging the channel chat is a great idea. I've had to go back into these logs various times to get bits of info. Making them public, though, is not such a good idea. This may be considered a violation of privacy to some (even though it's a public channel).

Keeping private logs is your choice and your business. If you choose to do so, don't make them public, unless (as stated above) that there's some awesomely extreme reason it has to be online.