I imagine that would be an interesting feature, but it is not presently a feature of phpBB.
With AOL's user reported spam policies I could see this becoming a bit of a problem though. About once every month or two I have to jump through hoops to appease the AOL e-mail gods because someone reported a topic reply notice as spam. There have been times I had considered banning any AOL addresses and suggesting those people using AOL create a yahoo mail account.
Yahoo groups does something like this where everyone essentially e-mails posts and everyone receives them.
You can however subscribe to as many topics as you like and be notified when new posts are added to those threads. At the bottom of every thread there is a link to subscribe to the thread and you'll then receive notifications the same as you would threads you started or participated in. (In you profile you can also specify the forums always notify you of new posts to threads you are participating in).
The board won't let you know of new topics you're not subscribed to, but if you check the "keep me logged in" box when logging in you'll see all new posts the minute you visit the forums. Not much more trouble than checking your mail, and saves you a step of having to first check mail then visit the forums.
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