There is simply no way that performing a quick stop will result in vortex ring state, because the rates of flow through the rotor are nowhere near the velocities required to cause vortex ring state. On the other hand, it is certainly possible to get yourself in trouble with the downwind quick stop if you don't carefully fly the maneuver. Why?
Because, when you bring the aircraft to a quick stop down wind, you first have to decelerate through 0 knots of air speed. And of course your power required its highest at 0 knots of airspeed, which you pass through somewhere short of the stopping point. This means the aircraft will sink a bunch at that 0 knot point, and ground contact is possible. Additionally as you pass through the zero knot airspeed, you actually begin accelerating rearward through the air so that the aircraft will start to try to point into the wind, becoming very unstable in yaw. This instability occurs right where the collective is being moved a bit due to the power required needs. As a result, you find yourself passing through the peak power point and dancing on the pedals at the same time. The chances of making a mistake are substantially higher than otherwise.
Typical quick stop problems include ground contact (especially the tail, because you are in a flare) and also poor yaw control. Overspeeds are more likely (big power changes) and sometimes there is a tendency for the helo to swap ends.
The old wives tale about vortex ring state being encountered while maneuvering near the ground simply will not go away. Let me specifically state that it is impossible to get into vortex ring state while maneuvering around the hover and performing maneuvers like a quick stop. Why? Because vortex ring state requires rates of descent of approximately 800 feet per minute to 2000 feet per minute, depending on the type of helicopter (actually depending upon the helicopter's disc loading.) if you achieve those descent rates near the ground, you have bigger problems than vortex ring state. The books that say that vortex ring state can be encountered in a 300 foot per minute descent are simply not correct.