I think this is more about them than a genuine protest. All it will do if it does work is show their might: I can’t see how it will effect meaningful change of any kind.
Will it work? It depends on how many recruits they get (real or virtual). I suspect they will disrupt some of the root servers, but I think the root server clusters will be able to handle it overall.
Other than the lulz, I don’t see this working out well for Anonymous. The perception of them may shift from We-Take-On-The-Big-Bad-Organizations to We-Are-Reckless-Vandals. They already took a hit when they backed off from taking on Mexican crime lords. This may result in them taking a further hit. But I am hedging here, obviously….we shall see the result soon enough.
For some details on this, see Pastebin.com
Smart People I Know 
Oh, please. Pastebin is not a reliable source for information. A quick search on twitter will tell you that people such as AnonOps have confirmed this is a hoax.
Just did “a quick search” of both their twitter account and their blog. Nothing on it being a hoax. Care to point to where it says that? If so, I will link to it here.
P.S. So how easy IS it to take out the root “servers”? Not very. As you can see from this: http://blog.icann.org/2007/11/there-are-not-13-root-servers/ there are lots and lots of redundant servers. It might be possible to take out the root servers for the domain of a small country, but taking out the root “servers” is another thing.