You're not learning C#, or VB.Net, or any language that matter, you're leaning the Framework. The big difference is you're leaning the classes, the life cycle (whether it be MVC or WebForms or whatever). The language isn't all that different from java in most areas in terms of syntax, it's the classes and what's in the framework that's the difference.
I'd say no, you don't need to learn C#, coming from java the language will be the easiest part, you'll learn the nuances as you go along. Learning what's in the framework itself, regardless of language, that's what will take a bit of time, not that's it difficult, there's just lots available. You'll never learn it all, and you don't need to, you learn what you need as you go along.
As a side note, there are projects out there that exist in both java and .net, for example hibernate and nHibernate, you could dig through these to see a decent comparison of what's available in both worlds and how some things translate across. I'm sure there are plenty more, but can't think of any big ones at the moment.