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Eventually bot will recognize the theme of the site and will display appropriate ads even on uncrawled pages.
In addition, when someone clicks an ad, they leave the page. If it were a chat site, they'd leave the chat. If that wasn't expected, they're likely to hit the 'back' button and to the advertiser the click would be wasted.
General chat isn't that good to target, but google media bot tries.
Honestly, the forum sis a good way to keep people clicking and coming back. Just think, if the ads are on topic and people are appreciating your chat they're more inclined to click an add and maybe even buy and discuss the product and service in your forum/community site so that others may click the add.
As always YMMV (your mileage may vary hehe)