No, it won't increase time automatically. But it could be the difference between hitting one's head directly on the pavement or having time to get a limb out to break the fall.

Although, I disagree on reaction time; 1 second is plenty of time to force the bike around a walker at 10mph. My avoiding a pile of bicycles catapulted directly in front of me at 30mph during a race was my only witness. Same goes for off road riding. I've had more than one rider wash out directly in front of my wheel at 10-12mph, I've yet to hit someone. But then again, that goes back to your being aware of your surroundings and riding within one's limits.