I would consider a university online class as a private space where only tuition-paying registered students can log in. In the US we have Family Educational Rights and Privacy Act Regulations (FERPA) that is pretty strict about student information.
If this were a discussion on a social media site, you might be able to justify coding posts from people who did not consent, but I think in a class that would be problematic.(See this continuum: http://vision2lead.com/?p=541. )
So I would say you might be able to do a very top-level coding looking at broad trends where personally identifiable information is not recorded (i.e. do people post more substantive content on Mondays or Wednesdays?) But when you get into the substance of what people are posting, you'd need to exclude data from those who did not consent.