You are right about the post count and such. Indeed that really can't be done easily. It probably could be done with some major hacking.
You could probably do SQL Queries periodically to update those counts on the main page.
I guess a script could be written to get the post count of xxxx forum and update the Board total for the xxxxteaser forum. You could run this nightly with a cron job. <shrug>
I'm thinking out loud.
(Which sometimes gets me in trouble.)
Really it's purpose is to let people know that there is something there that they don't see. If they see nothing, they don't know what they are missing.
Depending on what the forum is about... the admin could post "teaser" posts in there... giving people a sample of what they are missing.
As per limiting access to those logged in... yes, that's as simple as giving "no access" to the guest group. That way we aren't giving all our library here away without them at least signing up for a "library card" first.