There are a number of multirotors on the market which have propellers which fold at the hub, primarily to make storage and transport easier. Centrifugal force keeps the blade extended when the motor is spinning.
However, there is still a flexible coupling between the blade and the hub; what effect does this have on the aircraft during flight?
In theory, you can't accelerate and decelerate the props as quickly. If the motor accelerates, the props lower angular velocity keeps it from accelerating too quickly. Same for deceleration: if the motor decelerates, the prop's momentum makes it want to stay fast. It is only when the prop's position exceeds the motor's position, that the centrifugal force will slow it down.
But you have to consider that the angular velocity is quite a lot - therefore the centrifugal force is very high and the prop will only slightly move in its mount, thus not really affecting the flight all that much. Especially, when you consider that most drones with foldable props (e.g. DJI Mavic series) are "smart drones": They probably considered that during development and made it so that the motor speed is only raised and lowered slowly, so the effect isn't too noticeable. Plus, these drones are quite heavy so a tiny little change in prop speed will probably not have a big impact on the position in the air.
As you can see below, the propellers have different angles relative to the motor position. Obviously, propellers can only be designed for one direction of movement. Since the direction changes however, depending on whether it is accelerating or decelerating or at a constant speed, the uplift will be slightly reduced during speed changes of the props. 
Surprisingly, that flexible coupling is actually a good thing. If you look at helicopters, this is called a lead-lag hinge, and it allows the propeller to match flight loads when flying around. What happens is the blade advances in the hinge as it retreats in the airflow, and retreats in the hinge as it advances in the airflow.
(Watch a fully-actuated hinge on a helicopter: https://www.youtube.com/watch?v=Pu48f7s5Ru8)
This is because as the rotorcraft flies forward, the rotational velocity of the blades combines with the translational velocity of the aircraft to make for a different airspeed across the blades depending on where they are in their rotational arc.
Aerodynamically, this allows the blade to perform better in forward flight. In particular, as the blade goes faster to catch up it increases its airspeed and decreases the likelihood of a tip stall.
Structurally, the hinge removes all stresses about that axis[*]. In turn, reduced stress allows for a narrower blade root and a longer lived blade. In fact, it's very challenging to build a helicopter with a fixed root because the blades tend to fatigue themselves to death very quickly.
[*] By definition, a hinge is a mechanical device which provides for a rigid connection in all axes but the hinged one. A perfect hinge provides no resistance along the hinged axis.
