Basically I'm not for this Big Brother thing, but I had trouble with a user who turned out to have multiple accounts (that was years ago on 2.0.4). My forum was still very small at that time and it was on a free host. (say I had about 100 MB for the database). At a certain moment I had the impression than the database was growing faster than the forum. The culprit turned out to be table with PMs. I had no choice but to look into the database to see where all those PMs came from. It seemed that this user with all his extra identities was sending PMs to every newly registered member. Since it didn't stop I eventually decided to look into the database fields and saw that he was promoting his own forum and complaining about mine. This story isn't comparable to extremism or terrorism at all, but it makes me sympathetic to the topic-starter's idea.
What I eventually did was write a modification to backup all PMs sent (very easy, I think it was one of my first attempts at a mod). Later on I wrote a mod to read the PMs in that backup-table so that I wouldn't have to use phpMyAdmin anymore. Naturally I informed all my users that these modifications were made and installed (also explaining why).
The "problem" with this is that once users know this - the abuse stops. And I therefore doubt that this would in any way prevent terrorism. Anyway, a founder with some easily acquired knowledge could edit the phpbb files to prevent that data being stored in the first place (I have always found it harder to make something work, than to make it stop working ).