BuddyPress.org

Yes

Get the “More Privacy Options” over at wpmudev.org

http://wpmudev.org/project/More-Privacy-Options

Then in the Site Admin options go down to Site Privacy and select:

“Site can be viewed by registered users of this community only.”

It’s been a while since I set that part up, but I’m sure that’s all you need. If you want to have the main blog available, but not other blogs then use More Privacy Options, plus “New Blog Defaults” at:

http://wpmudev.org/project/New-Blog-Defaults

Set the Site Privacy to “Default: privacy managed per blog” and then in the New Blogs Default set privacy to “I would like my blog to be visible only to registered users from blog community” in the Blog Visibility section.

I think that is all you need for the setup you asked about.