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i have a site that has adsense block in header, and is accesed both for open areas and member areas. It is not exclusive to open or members.
I guess many sites have common adsense blocks that appear both in members and non members areas..
It's NOT against the TOS; indeed, I've asked Google for technical information to help me spot the bots specifically for this purpose.
However, if you serve these pages to the search bot that produces the Google search results, then you WILL, in all probability, get banned from the Google search. (They'll also be available in the Google cache, so negates the point of hiding them behind registration anyway).
I'd argue that a members-only PAID area, as you talk about, shouldn't have any ads there anyway...