Wow, darrensss - almost exactly what happened to me! Only my site is over 11 years old and pre-Panda was ranking at a PR of 5 - dropped to 0, now back at 3 but SERPS results still stink, leaving me another lost ship sinking...
Anyway, fascinating conversation, as I've been seriously thinking of taking that code off my pages, too. Like someone said, it's like inviting the enemy right smack into your home (and bank account) these days. I've been flip-flopping on this decision for about a year but now I'm going to try it, too. At this point I don't think it could hurt me any more than the Gmen already have.
I have another large site, about 9 years old that does better and I didn't do nearly as much optimization and link building on it - but never installed any Analytics code on it, either.
I understand why some think it's not possible, but maybe it's time to consider the possibility it is - this isn't the first place I've read this kind of thing in the past year. Just a thought. Anyway, thanks for all the input everyone. Will follow this topic, too, please keep us updated if you're trying this and I will, too.