Call me an idiot, but this is how I see it:
In my opinion, time and money would be much better spent on the 'improving security' bit than the 'trying to fight an extremely impulsive and loosely-structured entity' bit. Not only would that mean that governments and the like be protecting their information from more potential attackers, it has the added advantage of not provoking a large (relatively speaking) collective of hackers known to be pretty righteous about this sort of thing. Anonymous tends to mess with things it has a problem with, so announcing that you're going to try and infiltrate it, interfere with its operations and prosecute its members isn't going to go to end well for you, especially not if you try it via the internet, which is very much their home turf.
As far as the plausibility of infiltration is concerned, I'm not sure it would be all that difficult, but I'm not sure any information you'd acquire would be very useful, and certainly nothing to compromise any sort of operation.
So, in short, trying to infiltrate Anon would probably do more harm than good and any information gleaned wouldn't really be all that useful.