Just make the other passengers aware that this person is using his/her electronics while they are supposed to be turned off. Also, complain to the FA and note that you're afraid for your safety. If the guy insists on doing it, ask to make a formal complaint with the police at the airport where you are landing.

As someone said, provided that you are above 10k feet, BB's do have a no antenna mode and the email is stored on them. You can usually tell if they are active as the light on them will flash when they get new email. Reception is not very good at flight so I doubt anyone would use it to do that once you're above 10k feet. It would only drain the battery and they wouldn't really get a data signal.