Both coils need to be connected to a low impedance source in some way or otherwise the Qts (or Qes exactly) will change. It doesn't matter Qes-wise whether it is connected to an amplifier or just shorted. If shorted, it acts as an electrical brake but that braking action is necessary to keep Qes constant. Power handling might need to be derated. Sensitivity will degrade by 3 dB.
Now consider the following:
Qes = 2*pi*fs*Mms*Re/(Bl^2)
Where Qes is the electrical damping factor of the driver, fs is the free-air resonance frequency of the driver, Mms is the moving mass including air load, Re is the resistance of the voice coils and Bl is the driver motor force factor, N/A or T*m.
Namely, the Re/Bl^2 part should remain constant. If the other coil is not connected, Bl will be equal to the case where coils are connected in parallel but resistance is doubled. That means the Qes will also be doubled. If both coils would be connected in series, the resistance will be 4x to the parallel case but force factor Bl will be also doubled, since there is now double length of wire in the motor air gap, thus the Re/Bl^2 part remains the same.
Now since Qts is dominated by the electrical quality factor, it will be usually also increased by similar factor, because mechanical quality factor is usually much higher than electrical one, (something like factor of 10).
Approximate efficiency for typical driver can be calculated by
no = rho*Sd^2*Bl^2/(Mms^2*2*pi*c*Re)
Sd is the effective cone area and rho is the density of air, c is the speed of the sound.
So compared to parallel connected case, doubling Re will halve the efficiency and reduce the power sensitivity by 3 dB.
Regards,
Janne