Going to the website that's been taken down wouldn't raise support, no, but hearing and reading about it would make some people think, "Wow, what a ballsy move. Why did they do this? *Googles* Oh, this is more serious than I thought!", albeit not many people would do that. You are right in that the majority of people would dismiss it as just a nuisance though. But the small amount of people who learn more about the issue can still make a difference.
Besides, who doesn't know about SOPA at this point? If someone was up to date with the news, they wouldn't go on to the RIAA website and be surprised when they found out it was down. They would figure that some people got pissed and decided to be a nuisance.
Which is basically what Anonymous is all about. Being a nuisance.
I don't want to argue with you though, because you are right. There are much better ways to go about this.