What it might do is cut off recruitment. There's a spectrum of Anonymous folks, from the script kiddies who downloaded LOIC, and have it running on their parent's computer, all the way up to the serious folks who actually designed and architected the attacks. The serious folks know how to protect their anonymity well, and it's unlikely that any significant portion of them will be caught and tried. The script kiddies are pretty vulnerable though, and are going to get picked off by prosecution.
Thing is, there's an evolution, from LOIC downloader, to someone who understands the security concepts better, to those who are able to plan and mount real attacks. If you cut the script kiddie population down drastically, and make it hard to recruit people into Anonymous, then it's going to diminish the population of higher-up members.
The strategy ends up being just like a real war: attack and pick off off the soldiers, until the generals are exposed, then go after the generals.