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Ah, so we're adding to global warming by slowing our Phantoms down. I just knew it was a problem....Yes - that works fine for linear or angular kinetic energy in vehicles or tools, where the existing angular momentum of the system drives the electric motor, which then behaves as a generator and induces current that can be used to do other work, or charge batteries. However, the equivalent simple energy balance that you describe for the aircraft is incorrect, because you are forgetting the changes in kinetic energy of the surrounding air - see below.
In the case of propellers operating in a working fluid (air in this case), that could also be achieved, but only in very limited situations for an aircraft with no other source of lift. For example, if one stopped actively driving the propellers and allowed the aircraft to drop, then the airflow through the propellers would cause them to turn, rather than just stopping (equivalent to a wind turbine), and the work done by the airflow turning the props could be used to generate electrical energy in the motors. In this case one is converting aircraft potential energy (rather than kinetic energy) into electrical energy, but at least the principle is similar.
In the "active braking" case described, however, this isn't going to work, because rather than the motor drive being reduced and allowing the aircraft to coast to a halt (which would not work well anyway because most of the thrust is still needed to maintain altitude) energy from the battery is being used to produce extra opposite thrust to slow down the aircraft. More work is being done on the working fluid (the air), not less, so it isn't even reducing the power consumption of the motors, let alone allowing energy to be recovered.
The main reason that this is confusing, compared to cars or machine equipment, is that the energy partition is not as simple for an aircraft. In the former cases one can simply consider the linear kinetic energy of the vehicle, or angular kinetic energy of the machine, and if one reduces that by motor braking then one can recover significant energy by using the resulting induced currents in the motor windings. But in the case of a quadcopter, it's not simple motor braking - the props change the momemtum and kinetic energy of the aircraft by pushing air around - i.e. changing the kinetic energy of the working fluid in which it moves. As a result, most of the kinetic energy of the aircraft cannot be recovered by the props/motors and is instead converted (and lost) to increased kinetic energy of the surrounding air.
I don't have any analysis data right at the moment nor do I remember just what happens but you should be able to see what the motors are doing by looking at the log files in your viewer of choice. Does the voltage to the motors decrease? Increase?