'kay, first of all, as I understand it, the Like Box and the Like Button are not the same thing, and are used for different purposes. I use both - it's not an either/or.
The Like Box - think of that more as a roll call of people who have "subscribed" to your Facebook page. Everytime you post something on that Facebook page, they get an update in their feed. It's almost like having a mailing list. On Facebook. So the Like Box exists to persuade people to subscribe to your page on Facebook.
The Like Button is more for the users to share your site's content between themselves. So if someone 'likes' some content on my site, a link to it appears on their wall, and all their friends see that they liked that link, and (presumably) the friends go check it out, and if THEY 'like' it, then THEIR friends see it, and so it spreads. Facebook would have made this all a lot easier if they'd named things better
There's no way a Like Box is going to generate any duplicate content, and a Like Button - that shows up on the users walls, and I don't think Google even has access to that.
And to answer your initial question - nobody knows the effect it has on Google. I don't personally see how it can have much effect, because they don't get to see most of the data (and it's obviously driving them nuts that they don't - hence the +1 Button. Which, by the way, NONE of my tens of thousands of users have clicked on, while they're busy liking and tweeting stuff like crazy)
I use the Facebook stuff not with a thought of what it can bring me from Google, but because I want to make it as easy as possible for people to share my content. And if it takes ugly buttons and boxes to do it, then I put ugly buttons and boxes up.
Even if Google is using the partial data it may have, it's still going to be only one of hundreds of other factors. Not likely to make or break you.
[edited by: netmeg at 3:49 pm (utc) on Jun 24, 2011]