It's hard to say without knowing the exact circumstances. Personally I think it would help. If you see a car on the road headed your way as you're crossing the street it's pretty easy to tell how fast it's going, especially 5 mph vs 15 vs 30 vs 60. And if it's going fast your inclination should be to keep a sharp eye on it and maybe try to run out of the way if it appears as though it's not slowing down at a point when it should. But then again there are some intersections where you just can't see or keep track of all the traffic that could be dangerous to you, but on the whole I'd say it's smarter to do so than not, it takes little effort.
Indeed. I once saw a pedestrian step out in front of a moving police car with lights are sirens going. The walk light had just turned green. The police car had to slam on the brakes and lean on the horn to avoid hitting the idiot.