If half of what the lawyer said about their behavior is true, I don't see how they can possibly win the appeal. At this point they're throwing good money after bad.
They're definitely earning a reputation for secrecy and obstinance that is unbecoming of the position that they claim to hold, though I somehow doubt that many JWs will be affected personally by the news. Even if they see it, they'll just assume its "imperfect men" in the congregaion and won't bother to read enough to realize that it's a systemic problem, or that it's their donation money that's going to pay these victims (and indeed their money helping to fight against compensating the victims). Sadly, I well know that if I had seen the headline "Jehovah's Witnesses to pay $13.5M to sex abuse vitim" I would've just assumed that it was a civil case against an individual in the congregation and the reporter made a mistake in using the plural "witnesses." I certainly wouldn't have bothered reading the article.
I hope I'm wrong, but I don't think the average JW is sufficiently keyed into the goings-on of the world that they'll notice this at all. Sure, they'll lose some due to this, but I don't think the loss in membership will hurt as bad as the loss of money. I think these lawsuits need to win and bleed the org dry of money to have any hope of resulting in a rapid decline of the cult. Maybe I'm just in a pessimistic mood, though.
Edit:
I just thought of one caveat that might make all this have a much bigger effect. If the late-night shows pick up this news and make jokes about it, that will personally impact a lot more JWs than just having it on google news or CNN or whatever. People will turn off the news if they're not interested, but a 20-second long joke on letterman (that's over before you know it) will hit home and plant seeds.