The most current form of bodyarmor used by the military does protect against armor piercing rounds. Specifically, a vest can provide protection against one M2 Armor Piercing .30-06 Springfield round.
http://en.wikipedia.org/wiki/Improve..._Tactical_Vest
My personal opinion is that if I was engaging someone at close quarters and saw them wearing this bulky vest then I would probably aim for the head. Its difficult to say though because I would probably have between 1-2 seconds to react and fire.
Could it hurt wearing a plain windbreaker type jacket over the exterior vest? The only harm in wearing a windbreaker jacket is getting tangled up in it.