As far as copyright protection law goes, we here at JKS are not lawyers and we can't give you legal advice, but every writer has to come to their own decision about what they're comfortable sharing. In our classes and even in our 1:1 sessions, you can share as much or as little as you want, and as with anything, the more you share, the more educational benefit you will receive. That said, generally ideas are not copyrightable, but the execution of those ideas can be protected by copyright. (By the way, you want to use the US Copyright Office for that. WGA registration covers other stuff that's valuable once you sell your script, but only the US Copyright Office protects your copyright).
That said, in order to sell your script, or even get it read by someone in the industry, you're going to have to get comfortable pitching your ideas to all kinds of people. That's true for beginning writers, and even for professionals. It's just part of the inherent risk of the business. Jake wrote a great article about those risks and how to navigate them, which might be helpful as you make your decision.
We think you'll see once you're in our classes what a safe and nurturing environment this is. But, of course, if for any reason you go to the first class and in any way feel uncomfortable, all you'd need to do is let us know and we will be happy to refund your money.