Can you "reconnect" the Surefire lanyard?

I can't really picture what they mean by "the fastener is designed to break away if the lanyard or light is pulled on with extreme force." can you reconnect the ring if it "breaks"?

Short answer: no.

I don't know if the lanyard could be reconnected if the cord were jerked out of the plastic terminal. When I got my L4, the lobster claw clip wasn't even strung onto the paracord, it was just thrown in the bag. I saw no way to string the clip onto the cord without getting the plastic terminal off. I gently pryed open the terminal at the point where the cord enters the part and freed the ends of the paracord, I then strung the clip onto the line. I was able to reclose the the plastic piece back onto the ends of the cord. It seems to be holding quite well now.
I wouldn't consider this to be something that can be repeated without risking damaging the terminal beyond usefulness.

You can probably get away with it a couple of times. If the plastic terminal fails, they are cheap and easy to replace - I used to have to hunt for them, now Lighthound.com carries them.

I ended up in one situation where I had to test it - I was attending to an emergency when my U2's lanyard got caught in a door and I refused to slow down, I charged through with such force that one of the split rings turned right back into a straight piece of metal (thus releasing the light) at no time would I have been in danger though, I was holding the U2 in my hand with the lanyard trailing behind it, not around my neck or attached to any part of me.