No, if an induction motor (which is an electric motor that doesn't have brushes) stops turning for whatever reason, then you effectively have a short circuit through the stator. In that case, current through the stator will quickly exceed the amperage the circuit is fused down to, and you'll simply blow the fuse or trip the breaker that motor is on. As long as it's on a circuit that's fused down to 15 amps, the motor will just blow the fuse and then you no longer have power available to anything on that circuit, including the motor.

Take a look at the electrical schematic for an induction electric motor:

http://img.bhs4.com/a5/4/a54261670cf...a9a0_large.jpg

This one is a capacitor start motor, but a split phase motor's schamatic would be exactly the same, except that it wouldn't have a capacitor.

You have a Main winding and a start winding. The start winding is taken out of the circuit as the motor comes up to speed. If that were a DC circuit, you'd have a dead short through the main winding. The only reason the current through the stator in a real AC electric motor doesn't become excessive is that the main winding sets up an electric field through which the rotor windings spin. That action creates a current in the rotor windings, and the current in the rotor windings creates a magnetic field that opposes the current through the stator windings. This is why electric motor only draw a lot of current when they're starting. Once they're up to speed, the running current is actually quite low, making them highly efficient mechanically.

But, if you were to grab onto the rotor and prevent it from turning, you wouldn't have the electrical current generated in the rotor windings and there'd be no opposition to the current flow through the main winding, and the result would be that the current through the main winding would act like a dead short and quickly exceed the amperage of the fuse or circuit breaker that motor is on, shutting down electrical power to the circuit.

The motor would only go up in flames if it wasn't fused down to a lower amperage. If it were the convection fan motor in a convection oven that was on a 220 volt 50 amp circuit, then there could be 50 amps going through the stator, in which case it would probably get so hot the flammable parts inside it would probably catch fire. I've never had a convection oven, but I expect the motor of the convection fan has it's own fuse or fusible link so that if current through that stator got excessive, the fuse or fusible link would burn out. Otherwise, it'd be kinda dangerous and a potential fire hazard.