Simple answer. No.
A drone with fixed wing propellers such as the one you describe can not autorotate. For autorotation to work the pitch of the blades needs to be variable.
At the instant of engine failure, the main rotor blades are producing
lift and thrust from their angle of attack and velocity. By
immediately lowering collective pitch, which must be done in case of
an engine failure, the pilot reduces lift and drag and the helicopter
begins an immediate descent, producing an upward flow of air through
the rotor system. This upward flow of air through the rotor provides
sufficient thrust to maintain rotor rotational speed throughout the
descent. Since the tail rotor is driven by the main rotor transmission
during autorotation, heading control is maintained as in normal
flight. - https://en.wikipedia.org/wiki/Autorotation
A drone or multicopter with 6 or more propellers can continue flying as long as the thrust provided by the remaining propellers and engines is sufficient to keep it from falling.
The aicraft may however begin to rotate around its own axis. In normal flight there are an equal number of clock wise and counter clockwise rotating propellers. If a propeller/motor stops spinning the torque of these engines will no longer cancel each other out so in order to not descend the helicopter may be forced to accept a rotation around the Z axis. This same mechanism is used for turning a multirotor, lower the RPM of the propellers spinning in one direction and you will turn in the other.
I fly RC drones myself and have tested how my hexacopter behaves during a motor failure. The conclusion I came to is that if it was close to its carrying capacity it would rotate since it needs all the power it has and can't worry about rotation. But if it only carried a light load it woulden't rotate as it has power left over to compensate for it.
There are however a few attempts at making drones with variable pitched propellers
This however negates the pure simplicity that a drone provides as one of it's main advantages is that there are only as many moving parts as there are propellers.
In my opinion and others (http://diydrones.com/forum/topics/why-are-we-not-seeing-more-variable-pitch-quadcopters) the only way to provide a reliable drone is to have 6 or more propellers and lots of power to spare.