In a series circuit the same amount of current flows through all components. Since the led probably can only take 20ma, that is almost certainly not enough for the motor, so no you probably cannot do it that way.
Electricity flows from negative to positive, but that doesn't matter really. In a series circuit you can add a resistor in whichever position you want and it will do the same thing.
A different way to accomplish it is with a low value resistor in series with the motor. A certain amount of current flowing through it will create a certain voltage drop (ohm's law), so you use a comparator to sense this voltage drop and trigger when the current goes too low. The problem with that idea though is it assumes that when the motor fails it will be open circuit, when it could actually be short circuit, which could be overheat the motor or the drive circuit.