I'll give you my tuppence worth (
) on this Niall since I've a lot of experience with vB and Adsense.
First of all, Google will serve ads on any page you install adsense regardless of the content. It will show relevant content to the page for those pages that are cached on Google servers. If Google cannot see the content then it will not deliver a relevant ad. It also will not know whether you are breaking the T&C or not.
Google cannot scan a webpage of a private forum because there will be authorization required in order to access it. It also cannot give you a type of code for you to insert that can scan a webpage and read its content because this would be in violation of Data Protection and Privacy laws. Things that are private, should remain so for a reason. There's a file called robots.txt which you should have already placed in your root webserver which tells Google robots where to scan the site in order to cache it. If you don't allow them to enter the General then they cannot cache the webpage and learn of the content. By making it private on the other hand secures it even more from possible checks from Google employees. However Googles T&C's may not allow you to place ads on private forums. (I doubt they complained about the Newbie forums).
There is also the other option that Weaste mentioned in which you can determine certain pages where ads will be disabled. This is the safest and cleanest way of doing it and ensures that you don't break the T&C's. There's plenty options in the adsense CP.
However I still am in favour of a private sub-forum, even if you would use the option of disabling ads on some pages. A sub-forum where only mainstanders would have access to which could be used to WUM the press and post the usual tripe that isn't allowed on the public part of the site.