You are probably right, if indeed you smell it in the duct system because if it were a fan relay, that wouldn't be in the air stream. However, the smell you are getting may not be the motor but the high temperature of the Heat Exchanger
The simple first step would be to switch the thermostat from heat to off and allow it to cycle down then switch the fan to on and see if you get any blower as this uses a different relay in most cases to energize the fan (parallel) it may also use a different speed. If the motor is shot, it wont work on one versus the other.
If the motor doesn't work on either. Then you can go to the unit (turn the power off at the disconnect) with a meter and ohm the windings with them removed from the control. If they are open, then the internal overload of the motor is open or the windings are shot.
You may want to check the capacitor for the blower motor and see if it's OK. If it's swollen, it's bad, but if not you can check the capacitor with a meter using the mfd readings with it disconnected. If it shows it should be a 10mfd or 10u @370 vac, then your microfarad reading should be within 10% (9-11). Not all meters have this. Another test of the capacitor would be to set your meter to ohms and touch both terminals. At that moment the ohms should jump up and back down. Reverse the leads and try again. This test is not foolproof though.
Also while you're in there, see if the blower wheel spins freely to make sure the bearings have not seized.