It sounds like an unnecessary waste of bandwidth to me. People could have their tabs open without actually looking at them and you would still be using up the forum's bandwidth. That is, if it is done automatically. If it is done manually then, yeah, it would be a nice feature to have to save a second or two per load, but nothing crucial.
Actually this can be automatic and save bandwidth (not only not waste it) if done properly:
Something like infinite scroll can be implemented via jQuery and that could be triggered only when the tab is on focus and a scroll happens. Another option is to query regularly (every 30 seconds or so) for new posts only when the page is on focus (even if no scroll happens) but only a boolean would be returned indicating whether or not new posts are available on that specific thread (cache could be used server-side if several users are on the same thread). If there are new posts then a message would appear and the user would need to click on it to have them loaded. Gmail does this for new emails on the current conversation.
Only a few bytes would be queried only when the site is on focus. This would prevent a lot of users to hit F5 just in case, wasting a lot of bandwidth and -even worst- DB queries and other resources.
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