The vast majority of copyright infringement goes unchallenged. The fact that it's illegal doesn't mean people won't do it, whether on the internet or not. You've heard of torrent sites, yes?
This is not to mention that it depends on your specific area. It might not be illegal for someone in one country to post a transcription, but it might be illegal for someone elsewhere to do so.
If you want this definitively answered, you're going to have to hire a lot of lawyers. If you'd like to look at once piece of related law, see 17 U.S.C.A. § 110. I can't tell myself under what circumstances that would grant transcription rights, or if it does at all.