dc42:
I don't think so. The diode connected across the transistor is the wrong way round to conduct reverse voltage from the coil when the current through it is interrupted, unless it is a Zener diode.However, in an H-bridge with diodes across all the transistors (or the body diodes of mosfets), you're right, those diodes contain the back EMF by feeding it into the power supply.
The diodes are doing the same job in either position. the diode across the transistor is there specifically to protect the transistor from reverse transients from switching off an inductive load. The Diode across the motor would short the voltage spikes through just the motor and would stress other elements of the circuit less. The capacitor would be a good addition for either a motor or a coil, just make sure it has a high enough voltage rating for the spike.