Probably maybe...
O.K. "bullet proof" goes back to the days of armor which wasn't very and that got it unpopular much... Why spend a couple years income on tin suits for man and horse when they can be penetrated??? Brits did that nicely at Crecy and Portiers with the "cloth yard" (32 inch) arrows with steel tips that are lubricated with wax (probably bees wax)... and the long bow... and fired in flights of hundreds... 6 per minute was a leisurely pace...
Until recently the body armor was plates, mainly metal, very heavy and while "o.k." not likely to be worn except in the most obvious of situations. Knew a soldier from Korea told me about bakelite/plastic plates but they did not overlap. Bullet hit the plate, great. Went between plates... -0- help. And you were all sweaty from the canvas jacket with the plates...
In US the kevlar has been around since Viet Nam. High friction fibers.
It works like a "pitching cage." The projectile is "caught" in the super strong fibers by the friction of the fibers on themselves... #1). You get a whopping bruise under the armor. If gun is bigger than .38 Special, you spend the night in the hospital for observation against clots, etc. Bruise problems. Impact trauma. #2). If it is wet, forget it. It is about worthless. The friction is lost. Thus the plastic bag container and dislike by officers in hot climes. #3). If hit, the maker usually gives the wearer a new one cause each "hole" is good for about one hit and then, strength lost, worth about as much as a bulky sweat shirt if hit a 2nd time in the same spot. (Most crooks are not that good a shots, but bad luck is back luck.)
In the scene you present, well... if the bad guys were so stupid that they did not notice the officer being much less harmed by the shots to the body and shift aim to the head... bad guys now know to shoot for the head/neck in USA thanks to news coverage of cops "saved" by a vest... then the officer might well have gotten his gun into action and survived or taken a few with him.. MIGHT! But 3 against one is bad odds anytime. And usually, however messed up the killers are on "courage," one will be behind... I would guess his chances at 40%/60% but unless he knew the killers and was on guard... He's toast. Goes with the territory. As was, chances 20%/80% against living. Enjoy.